A quick guide to inequalities

Make sure you know your symbols:
< - less than
> - greater than
< - less than or equal to
> - greater than or equal to

To graph an inequality, use an open dot for > and <. Use a closed dot for > and <.

Use the same rules for solving equations to solve an inquality (get the variable by itself by using the inverse operation) - just be sure that you're not using an equals sign (use the inequality symbol instead).

*VERY IMPORTANT*: When multiplying or dividing each side of an inequality by a negative number, reverse the direction of the inequality symbol!!!

Example:

-3x < 12    ---> We need to divide both sides by -3 in order to get x by itself.

-3x < 12   
-3      -3

x > -4       ---> Be sure to FLIP the inequality sign!!!

The Very Mathtastic, Super-Quick Guide to Equations

To solve an equation:

1. Remember, your mission is to get the variable all by itself. .:Cue Mission Impossible theme:.

2. To do this, use the inverse operation. Ask yourself, "What's happening to the variable?" and then
    do the opposite of that to both sides. Remember that addition and subtraction are opposites, and
    multiplication and division are opposites.

3. Your equation will now tell you what the variable equals.

Examples:

6 + y = 17  ---> What's happening to the variable? We're adding 6 to it. The inverse operation
                          would be to subtract 6. DON'T FORGET - YOU MUST DO THE SAME
                          TO BOTH SIDES.

6 + y - 6 = 17 - 6  ---> Solve both sides of the equation.

y = 11

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-2 = a - 10  ---> What's happening to the variable? We're subtracting 10 from it. The inverse
                          operation would be to add 10.

-2 + 10 = a - 10 + 10  ---> Solve both sides.

8 = a
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3x = -15   ---> Since we're multiplying the variable by 3, the inverse operation would be to divide
                        by 3.

3x = -15   ---> Remember, the fraction bar means "divided by."
3         3

x = -5
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m = 3   ---> Since we're dividing the variable by 9, the inverse operation would be to multiply by 9.
9

9 x m = 3 x 9   ---> Don't forget, a 9 on top and on bottom cancel each other out.
      9

m = 27
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Well, folks, there you have it. Just make sure you:
1. Use the inverse operation
2. Do the same thing to both sides
3. Get the variable by itself
4. Check your answer by plugging that value into the original equation (in place of the variable)