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### Contributing Overview

Slader is an academic community for students, by students. Users view and share answers and explanations for high school math and science textbooks, join academic classes, post homework assignments, and discuss those assignments online.

You contribute solutions to Slader. Your friends, classmates, and peers across the country can view, comment, and expand upon them.

Solutions consist of an explanation and a result. All Slader users and guests can see results from any book for free. When a user views the full solution, we call this a solution view. To view a solution, users must either have purchased solution views or have subscribed to solution views. Every time your solution is viewed, you earn gold. The more your solutions are viewed, the more gold you earn. Read more about gold in the next section.

You can add a solution on the website using our equation editor. If you have an iPad, you can download our free application. The iPad application includes a simpler and more complete editor. You can download it from the App Store here. If you kept your homework from this past school year, you can snap a picture of the work with your iPhone or iPod Touch.

You can use any high-school level math or science textbook that you own. Can't find your book? Ask us to add it here.

Our contributors are a huge part of Slader's success, and we're grateful to every one! Send us suggestions or feedback any time at . You can also join in the conversation on our contributor discussions.

### Earning Gold

Gold is the currency here at Slader. Users can earn gold by purchasing it or having their solutions viewed.

When any paid or free user first views the solution for an exercise, the author of the top solution (most number of up votes) will receive 1 gold.

Users can redeem gold for cash on their account page. The redemption rate is 10,000 gold for $10. All gold that you earn from solution views are redeemable. We expect that a popular exercise from an average textbook will earn$0.50 a year (which is conservative, since that is only 500 views). Multiply this across hundreds of written solutions. You can earn lots of money, year after year, for writing strong solutions now.

A really popular textbook may have several hundred thousand students using it. Let’s say you have 4000 of those people viewing your solution. You would receive 4000 gold for that solution, or $4.00. Multiply this across a number of completed popular solutions for your total annual earnings. An entire chapter of work is about 500 exercises. Over time, if 100 of those exercises are particularly popular, you could easily earn$400 a year for the chapter. Your other exercises will also earn revenue. Multiply this across a number of completed chapters for your total annual earnings.

Remember to account for free views. All Slader users get a certain amount of free views a day without having to purchase anything. This means that not everyone will actually pay to view solutions. However, you receive your royalty on every unique view, regardless of whether the user pays or does not. Free views will account for most of the traffic on a specific solution.

You can also earn royalties by recruiting your friends as contributors. You receive 20% of all of your recruits' gold earned from their solution views. (That revenue isn’t taken from your recruits. They still make 100% of what is owed to them. You simply receive an extra 20%, since you recruited that contributor.) If you recruit several people, it is possible that their earnings combined will earn you more money annually than your own solutions. More about referrals here.

### Textbooks

Slader currently offers high-school level math and science textbooks. Our core focus is math. We have over 250 math textbooks, from pre-algebra to discrete math. If we're missing the book used at your high school, you can send us its details. New books go up on the site within a week of the request.

We recently added two physics textbooks. If you're strong in the sciences, let us know! We'd love to talk about adding your chemistry, biology, or earth sciences textbook via email at: .

Due to copyright issues, we do not reproduce textbook questions on the site. You must have a textbook to answer questions.

You can also browse a textbook's table of contents to see how many unsolved problems it contains. Listed for each chapter is the percent of problems completed in that chapter. If you click on the + symbol next to a chapter, you can see the number of unsolved exercises in each section. Click here to browse our textbooks

### Choosing Exercises

What types of solutions normally have the most page views?

• word problems
• even problems (since even answers don't usually show up in the back of the book)
• challenging problems from the middle of a section
• problems that require graphs or sketches
• proofs

What kinds of solutions normally have the fewest page views?

• true/false problems
• vocabulary problems
• the beginning problems
• end-chapter challenge problems or extra sections
• Find the problems that you believe a teacher would assign for homework! Many teachers focus on repetition to hone skills. See that section of ten problems that all look the same? A teacher probably assigned at least one or two of them.

Although it is tempting to choose the easiest problems to solve and forget about the hard problems, the easy problems are not necessarily the ones that receive the most views. Your goal is to write good solutions for moderately difficult problems. You should think about how you want to spend your time. Ten vocabulary problems combined might receive 100 views a day (combined). One well-written solution for a mid-chapter problem might, by itself, receive 100 views a day.

You can browse a textbook's table of contents page to see which sections have the most empty exercises. Each chapter has a barometer showing the percent of problems completed in that chapter. If you click on the + symbol next to a chapter, you can see the number of unsolved exercises in each section.

### Writing Solutions

Slader is a resource for students who need help with their textbook homework exercises. Solutions should be clear and easy to understand. Even if a problem seems simple for you, it may be difficult for someone else.

As a Slader contributor, you are a tutor. You do not have to mimic the textbook examples. (We 100% believe that students can articulate problems better than textbook authors can. You aren't an impersonal book of answers - you're a tutor, an aide, and a guide.)

All solutions need:

• the steps needed to reach the answer
• some form of written explanation to describe how you achieved the steps

Please DO NOT repeat the problem statement from the textbook. This is a copyright violation. All students looking at the math section of the website will already have the problem statement in their textbook. For instance, if the textbook prompt was x+y=90:

The template already indicates that users should see their textbook for the problem statement; students will also only look at problems that they have the textbook for.

Our best contributors submit solutions that are clear, well-explained, and show each step of the problem. Good solutions are also conscious of the level of the textbook. When you write a solution for an algebra problem, you should show every step. Calculus students, however, are much more familiar with simplifying equations. Write a solution for the student that will view it. Try to think like a tutor!

Sometimes you may not realize the many decisions that you make when answering a question. Are there many different ways to solve the problem? Which one is the best or the most efficient? Why did you choose that method? Imagine that you are actually talking to a friend or a classmate who is taking a Geometry class. What would that friend need to know?

Don't write a solution that you would turn in to a teacher. Write a solution that you would hand to a friend who needs help.

Here's an example of a good solution. The exercise prompt here gave three equations and asked the student to solve the system.

This solution follows our suggested guidelines. It:

• starts from the first step of the exercise
• clearly shows each step at an Algebra-level understanding
• explains why the exercise is solved in a certain way

If the exercise asks for a graph or an image, you can add those directly into the template.

We pay contributors 1 gold every time their solution is viewed by a different user. The Slader community rates each submitted solution on a scale from 1 star to 5 stars. Better solutions are rated more highly (nearer 5.0) and appear at the top of the page, and solutions that are not as good are pushed down to the bottom of the page. The author of the solution with the highest rating will be the only one that receives gold. Read more about our gold policy.

The better and more thorough solution you submit, the more likely it is to stay on top forever! Write a good solution now so that you can receive that gold later.

If your solution is good enough to remain on top year after year, you will keep earning money every year for years to come. And, as our community grows, your income will increase. We estimate that popular solutions could earn more than $4 per year. Multiply that by the amount of solutions you contribute overall. All it takes is spending a few extra minutes now to create a great solution that won't be challenged. ### Our expectations 1. We do not accept any copyrighted material. No piece of the original exercise can be in your solution. Start from the first step of the problem. A user looking at your solution will have the exercise right in front of him, so you’ll need to explain how to get to the next step without repeating anything the book says. Work copied from other websites is unacceptable. However, pictures of graphs that you've generated (including those on WolframAlpha) are fine. 2. You must show work - the final answer as your work will not suffice. We do not accept solutions without explanations. Keep in mind that someone viewing your solution is still learning the math behind it. For higher-level exercises, you are still expected to show as much work as possible, but your explanations do not need to address simple algebra used in your solution. Write solutions at an appropriate level. 3. Place all math inside two$ signs. This way, your math will always be easier for other users to read. Please use \dfrac instead of \frac when your fractions appear tiny and are tough to read. Avoid using “/” to denote a fraction. Although “/” is a valid indication of a fraction, once you have multiple fractions within an expression, it becomes much easier to use \dfrac to be certain that you’re typing in the exact expression you need.

4. Always use proper punctuation, capitalization, and grammar. Correct spelling is also a must!

5. If you are working with a Geometry book and are writing proofs, change the "Work" and "Explanation" labels to "Statements" and "Reasons".

For more helpful information on contributing, check out our FAQ, or get some great information on our Editor guide.

The most popular way to add solutions to Slader is via the equation editor. The editor is built into the website, and you can access it by clicking on any exercise.

If you have an iPad, you can download our free iPad application. It has its own built-in equation editor, which includes all symbols and expressions found from pre-algebra to discrete math. The iPad equation editor is a preview of what the web-based equation editor will soon look like.

You must have an account to access the iPad application. If you haven’t already registered on the site, you can create an account. Otherwise, use your Slader log-in and password.

To create an account on the iPad, tap the app, then hit “Create an account.” This will take you to the default browser on your iPad. You must check your email to activate your account.

The textbooks that appear on the iPad application are the textbooks listed under “My Textbooks.” You can add a textbook through the application by tapping “Add +” on the top left corner. You can then browse all exercises and exercise groups within the textbook.

The iPad application is better for contributors who do not want to work with LaTeX, the math markup language that our web editor uses. The iPad also has several features which have not yet been added to the site. You can save templates for exercises and use TextExpander within the app.

iPad users can also work on exercises offline. To set up this feature, first go online, then tap your book. Once all of the pages have appeared on the screen, you can turn of your internet connection and work on exercises from that specific book. When an iPad user connects to the internet, all solved exercises will be synced to our server.

Facility with the web editor and the iPad will vary from user to user. Test out each method to see which is most efficient for you.

The most popular way to add solutions to Slader is via the equation editor. The editor is built into the website, and you can access it by clicking on any exercise.

You can also take pictures of written work using your iPhone.

However, uploading solutions with the iPhone can be extremely cost-effective. Taking pictures with your iPhone is an extra 10 seconds per picture. You might be able to upload 5 detailed iPhone solutions in the time it takes you to write 1 detailed web editor solution.

iPhone solutions are unlikely to remain the top-voted solutions. This means that they are less likely to earn you gold over the subsequent school year. Therefore, we suggest that you upload with your iPhone only if you have a significant amount of homework stored from the last school year.

It is important to take a good picture and ensure that your solution is readable. If the picture is not clear and the solution is not easy to read, it will be rejected by the moderators.

Tips for taking a good picture:

• Make sure the solution paper is well-lit, but the writing is not washed out.
• Take a picture of only one solution at a time.
• Make sure the entire solution is visible in the picture.
• Align the top of the solution with the top of the picture.

Facility with the web editor and the iPhone will vary from user to user. Test out each method to see which is most efficient for you.

### Using the Equation Editor

Slader has its own unique equation editor. We’re constantly improving the web editor and adding new features. The editor is our top priority. If you have suggestions or feedback, please email us . (This includes button requests and request for new features.) If you have trouble with any aspect of the editor, we are on call to help you.

If you are using Internet Explorer, the Slader website will ask you to install the Google Chrome Frame plug-in. This is the only way the equation editor will work in IE. If you still have issues, please try opening Slader in Chrome, Firefox, Safari, or Opera.

The equation editor uses a math markup language called LaTeX to display your work. LaTeX can look scary, but is very easy to use. Until our editor is fully upgraded, you should know a little bit about LaTeX and the way it works.

When writing in LaTeX, the beginning of a math expression is signified by a dollar sign, $. The end of the expression is also signified by a dollar sign. Our editor will recognize that everything inside the dollar signs is an equation that it needs to render, or display as math.$x+5=10$Dollar signs act like parentheses do. You must make sure that there are an even amount of dollar signs in your problem! If you add a$ at the front of your expression but forget to add one at the end, your expression will not render. The editor updates in real time, so you might see a red X while writing your solution. Make sure that your expression has rendered before you move on to the next cell.

Only elements inside the dollar signs will be converted into LaTeX. You can add normal text in an explanation alongside math.

Simplify $x+5=10$ by subtracting $5$ from each sides.

DO NOT put normal text inside dollar signs. You will see this problem:

$Simplify x+5=10 by subtracting 5 from each side.$

Since everything is inside of the $s, the editor thinks that every letter is a variable. Please check your LaTeX to see how it renders before you finish an exercise. Pressing a button at the top of the equation editor will add a LaTeX command. LaTeX commands tell the editor that it needs to insert a special character. It is possible to write nearly any math expression in LaTeX, though some are more complicated than others. The most common math functions are listed at the top as buttons. When you press a button, it will insert the LaTeX command. Every command consists of a backslash (\) and a unique word. You must have a \ to insert a command. Otherwise, the editor will think that you are simply inserting variables (as seen above, where the words run into each other). The very first button is a multiplication sign:$\times$This displays differently from the letter x. You can also add other operations using the button, like so:$8 \times 7x \div 9$You do not have to put a space in between LaTeX commands and your variables/numbers, but it is easier to see problems with your LaTeX code if you do. Spacing does not affect how the expression renders. You could put ten spaces between \times and 7x, and it would render the same way. One basic LaTeX command is \dfrac, which inserts a fraction. Pressing on the editor will insert:$\dfrac{a}{b}$The default numerator is a, and the default denominator is b. You can put any expression into the numerator or the denominator. Just make sure that the braces fully enclose your expression.$\dfrac{7x+10}{2y \div 8} $This principle works with the exponent button as well.$a^{b}$Just like with fractions, you can put any expression into the braces. You can even put another LaTeX command inside the braces. This becomes tricky because you must ALWAYS have an even number of braces and dollar signs. Otherwise, your LaTeX will fail to render.$7^{x+8}7^{\frac{x+8}{2}}$(\frac is used here instead of \dfrac because it looks better in exponents than \dfrac does; \dfrac’s function is to make your fractions more readable, and you should use it in all other scenarios.) Note that there are an even number of braces and dollar signs: This is the most difficult part of writing LaTeX. While finding new commands is not particularly difficult, it is sometimes confusing to correctly “nest” all of your expressions in the right braces, brackets, parentheses, and dollar signs. If you are having trouble, you can check your expression in a parser like mathurl. Nesting is totally dependent on the user. If you highlight an expression and press a button, the button command will replace your previous text. When you write in the equation editor, you write plain text LaTeX. If you want to nest using buttons, it is best to start with the outermost commands and work your way in, clicking buttons to add commands inside of brackets. You can enter multiple math expressions in one cell of the template. Just enter \\, and the next equation will show up on a new line. Entering multiple lines into one cell can increase your efficiency. If you want to simplify an equation, you don’t have to create a new row of cells for each simplifying step:$x+7=12$\\$x=5$This expression can also be written as$x+7=12 \\ x=5$. Just make sure that the number of dollar signs is consistent. The \\ command also works in the explanation cells to create paragraphs. Entering \\ will create a line break anywhere you insert it. Most of the basic keys on your keyboard will display correctly if you enter them into the editor. The lesser than or greater than signs should be typed (> and < on your keyboard). To enter a dollar sign ($) or a percent sign (%), you must “escape” the symbol. Dollar signs and percent signs cannot be entered using only the keyboard and the $or % key. (You can use one of the buttons at the top of the editor, which will escape the symbols for you.) LaTeX uses both$ and % as indicators. Therefore, you must add a \ to get the $or % to render:$ $8$
Does not render. (LaTeX sees you have an uneven amount of $.)$ \$8$

Renders! LaTeX only sees two dollar signs, not three.

$75 \%$

Other less common symbols that must be escaped are & and {}. LaTeX uses the curly brackets {} to nest, so they will not display. You must escape them on the left: “\{“ and “\}.”

Quotation marks do not come out correctly in LaTeX or in the Explanation box, even when dollar signs are not in use. To get correct double quotes (“), use a left and a right pair of single quotes:

Scott says he is responsible.''

To get the single left quotes, hit the ~ button twice: . To get the right quotes, hit the apostrophe button twice: ‘’.

Although trigonometric functions such as sine, cosine, and tangent can all be typed manually, they also have LaTeX commands. These commands should be used so that the trig functions do not display as variables.

This is correct:

$\sin \frac{\pi}{2}=1$

This is not:

$sin \frac{\pi}{2}=1$

Since you do not have a \ denoting a LaTeX command in front of sin, the editor assumes that “sin” is a variable. Please insert \ before all of your trigonometric functions. The editor buttons can do this for you.

At the end of the guide, we’ve compiled a list of common codes and their render. If you can’t get a particular LaTeX command to render, please email us! We’ll add a LaTeX package for you. Included in the LaTeX library are some common.

### Graphs, Images, and Supplemental Materials

Currently, it is not possible to create graphs or images (such as drawings, number lines, or diagrams) directly on the Slader site. You must create graphs or images in another program, then save them as a JPG, PNG, or GIF file. We do not support other file types at this time. Ideally, your images should be smaller than 4MB.

To add an image to your solution, choose the cell in which the image will appear. When the web editor appears, you should see an option to “Attach an image.” Choose the file from your computer. The image will appear in the cell immediately after upload. If you are having trouble uploading an image, let us know at .

Graphs and images cannot be placed in the result field. Users pay gold to look at solutions (your entire explanation), but not to look at answers. Graphs and images are premium content, and take some time to create. By placing graphs and images within solutions only, we are protecting your interest in your work. Users must purchase or subscribe to solution views to look at content that takes you longer to create, and thus you are more fairly compensated for your time.

Instead of adding a graph to your result field, write “See solution for graph.” This also applies to proofs and paragraph-length answers (they take longer to create, and we want to protect your interest). If you aren’t sure about placing your answer in the result field, you can ask a moderator by emailing: .

Each image must be placed in a different cell:

We currently do not support multiple images in one cell. You can, however, write text or a math expression in the same cell as the image. A long text piece will wrap with the image.

Graphs can be created on several external websites. Wolfram Alpha and this site provide easy interfaces for graphing. On Wolfram Alpha, you should take a screenshot of your graph and save it as an image file. MathWorkSheets will allow you to save the graph as a PNG file by clicking “Save File” below the graph.

Images (such as shapes for geometry, number lines, etc) can be created on GeoGebra or other similar programs. GeoGebra is a free downloadable mathematics software. If you are skilled enough to create good sketches, you can draw a diagram or shape on paper to use in your explanation.

On the iPad, we suggest OmniGS, Quick Graph, and the Wolfram app.

You are welcome to use whatever program you would like to create images and graphs, as long as they are legible and professional. Contributors have utilized a wide range of programs, including Excel and the Office suite.

### Moderation

Solutions are checked by a team of trained in-house moderators. Every solution must be moderated before it can earn royalties. Once you press “Finish Now” at the top of a solution, it enters our moderation queue. The solution will appear with a red background, both to you and to others browsing your textbook. You can still edit and add content to a solution once it has been submitted, but this will push it to the back of the moderation queue.

Moderation usually takes about 48 business hours. This period may be slightly longer or slightly shorter depending on the volume of solutions submitted on a particular day. Since Slader is located in New York, it is most likely that your solutions will be moderated during daytime hours on the East Coast. If a significant amount of time has passed, please read over the guide and then direct any remaining concerns to .

Submitted solutions will be approved if they contain an explanation and a result. Both fields must be filled out. Solutions that consist of only a result will not be accepted. Solutions that repeat the same thing in the explanation and in the result will not be accepted. Solutions that do not contain math expressions or are not relevant to the exercise will not be accepted.

Moderation ensures that spam content cannot be added to Slader. We take our commitment to education very seriously, and we will not approve solutions that do not meet our minimum standards.

If one of your solutions is rejected, you will receive an email notification. (You can also see your moderation history on your submitted content page.) A rejected solution can be edited and re-submitted for moderation.

If you would like feedback on your submitted content or are confused about a rejected solution, please contact us! We’re a small and personal team, and we are more than happy to help with moderation guidelines. You will be able to talk directly with the person who has moderated your content and has spent time reading over your solutions.

Though it is easy to write short solutions that will meet our moderation standards, we have lucrative incentives in place to reward you for writing great solutions. You can read about our incentives here.

### Referrals and Recruits

Your recruit will earn gold for solution views, and you will earn 20% of that gold. This gold IS redeemable for cash.

The 20% recruiting gold are based solely on their solution views. You will not earn 20% of everything your recruit earns. You will NOT earn 20% of the 20% they earn for their recruits.

Recruiting a lot your friends is the easiest way to earn a LOT of gold. You will earn the 20% for each one of your recruits, and there is no limit on recruits. You do absolutely no work, and you still earn gold, which is redeemable for cash. You could earn hundreds of dollars a year for doing nothing more than recruiting several of your friends.

Recruiting is easy, and it will earn you real money. Send a link to your friends.

### Payouts and PayPal

Slader's currency is called Gold and is redeemable for cash. To determine how much gold you have, look at your submitted content page. Under “Turn your gold into cash,” we list your total redeemable gold.

Redeemable gold is credited when you:

• Solve a solution that has had a bounty placed on it (gold amount varies)
• contribute a solution, and it is viewed
• recruit a friend, and someone views your friend’s solution

All payout requests must be for at least 10,000 gold. So, while you can request a payout for any amount over 10,000 gold, you must have a minimum of 10,000 gold (10) to request a payout. The same will hold true for any future requests. Currently, we send payouts via PayPal. It is free to sign up for PayPal. If you absolutely cannot create a PayPal account, please contact our team to learn about other options. To request a payout, head to your submitted content page. Under “Turn your gold into cash,” click to request a payout. This request goes directly to our team and the gold amount is deducted from your ledger. Once the request is approved by Slader, PayPal will then process your request. You can find out more about gold in our gold section. ### LaTeX Library We currently display the most frequently used LaTex symbols on our Equation Editor. Even more buttons are coming soon, but here's a library of LaTeX symbols you might find useful. Use ''ctrl + F'' to search for a specific symbol. Remember to use dollar signs! To see what a symbol looks like, click on it and you'll be redirected to its mathurl generated image. If clicking on it does not work, it means that the mathurl image does not exist. For examples on how to use matrices and align functions, go to the end of the list. Symbol LaTex - Click to see sign \\$
absolute value \left| a \right|
alpha \alpha
ampersand \&
and \vee
angle sign \angle
approximation (two tildes) \approx
arc \stackrel{\frown}{AB}
arc cosine \arccos
arc cotangent \arccot
arc sine \arcsin
arc tangent \arctan
beta \beta
congruent \cong
cosecant \csc
cosine \cos
cotangent \cot
cursive l \ell
degree symbol \textdegree
Delta \Delta
division \div
dot \cdot
dot dot dot \dots
double arrow \leftrightarrow
empty set \emptyset
equals sign with tilde \simeq
for every, for all \forall
fraction \dfrac{a}{b}
greater than \textgreater
greater than or equal to \geq
in \in
infinity \infty
-infinity -\infty
integers \mathbb{Z}
integral \int
integral from a to b \int_{a}^{b}
integral from blank to blank \int_{a}^{b}
integral over a closed path \oint{a}^{b}
integrate f from a to b \left[ f \right]_{a}^{b}
intersection \cap
iota - identity relation \imath
left braces \left\{
left bracket \left[
left parenthesis \left(
left/right braces \left\{ \right\}
left/right brackets \left[ \right]
left/right parentheses \left( \right)
less than \textless
less than or equal to \leq
limit with arrow \lim_{x \rightarrow a}{f}
line break \\
ln (natural log) \ln
ln equivalence \ln x^k = k \ln x
log \log
log base a \log_a x^k
log equivalence \log_a x^k = k \log_a x
long division (polynomials) \polylongdiv{x^3+x^2-1}{x-1}
mu \mu
multiplication \times
natural numbers \mathbb{N}
negation of \sim p
not congruent \ncong
not equal to \ne
not parallel \nparallel
not, negation \neg
notation for a line \overleftrightarrow{A}
or \wedge
over line; notation for a line segment & complement \overline{A}
parallel \parallel
partial derivative \partial x
percent \%
perpendicular \bot
pi \pi
plus or minus \pm
power set symbol \wp
predicate equivalence \equiv
prime \prime
product notation with limits \prod \limits_{i=1}^N x_i
proper subset \subset
proper superset \supset
rational numbers \mathbb{Q}
real numbers \mathbb{R}
right arrow \rightarrow
right braces \left. \right\}
right bracket \left. \right]
right parenthesis \left.\right)
right\left braces \left\{ a \right\}
right\left brackets \left[ a \right]
right\left parentheses \left( a \right)
secant \sec
sigma \sigma
similar to \sim
sine \sin
specific root \sqrt[3]{x }
square \square ABCD
square root \sqrt{a}
strike-through-diagonal \cancel{}
subscript D_{x}
subset \subseteq
summation \sum
summation with a and b \sum_{a}^{b}
summation with limits \sum \limits_{k=1}^N k^2
superscript a^{b}
superset \supseteq
synthetic division*** \polyhornerscheme[x = -3]{6x^3 - 4x^2 + 17}
tangent \tan
text insert \text{some text}
there exists \exists
there exists only one \exists!
therefore \therefore
theta \theta
triangle \triangle ABC
union \cup
vector arrow \vec{AB}

Examples!
Example: Addition or Subtraction \begin{align*} \\
3.47 \\
\underline{-0.92}
\end{align*}
Example: Addition or Subtraction in Equations \begin{array}{ccccccc}
2.2x&+&5&=1.2x&-4 \\
-1.2x & & & -1.2x &
\end{array}
Example: Systems of Equations \begin{displaymath}
\left\{ \begin{array}{lr} x + y = 50\\
x + 43 = 2y
\end{array} \right.
\end{displaymath}
Example: The Matrix* \begin{bmatrix}
a &b & c \\
d & e & f\\
g & h & i \end{bmatrix}
Example: The Determinant* \begin{vmatrix}
a & b & c \\
d & e &f \\
g & h & i
\end{vmatrix}
Example: Augmented Matrix** \left[\begin{array}{ccc|c}
a&b&c&d\\
e&f&g&h
\end{array} \right]
Example: 6 Trig Identities \begin{align*}
\sin x &= a & \csc x &= b \\
\cos x &= c & \sec x &= d \\
\tan x &= e & \cot x &= f
\end{align*}
Example: The Align Function* \begin{align*}
10x &= 2x + 4 \\
10x - 2x &= 4 \\
8x &= 4 \\
x &= 2 \end{align*}
*This expression does not require dollar signs.
**The number of c's indicates the number of columns. "\\" indicates the start of a new row. This expression does not require dollar signs.