One step problem.

Divide both sides by -3

Two Step Equation.

Multiply both sides by 2

One Step Inequalities

Multiply both sides by 10

Sign is "Greater Than or Equal To"

One Step Inequalities

Divide both sides by -10

Flip the inequality sign!

New sign will be Greater Than.

Negative Number Operations

Change to adding a negative 6

Combine -17 and -6 to make -23

Order of Operations

Inside parentheses first (subtraction), then exponent, then multiplication

Order of Operations

Treat division bar as grouping, perform operations on top then divide.

Converting from improper to mixed

Figure how many whole numbers are represented by dividing the numerator by the denominator.  Then subtract the parts that represent that whole number from the numerator, and leave the remainder over the denominator.

Example:

17/4   there are 4 wholes in there, so take away 16 parts, leaving 4 1/4

Coverting Mixed Fractions to Improper

Multiply the whole number by the denominator, then add to the numerator to get the total # of parts over the denominator.

Subtracting Fractions

First step -- convert to common denominators!

Convert 5/3 to 10/6

Convert 1/2 to 3/6

Then add the numerators

Multiplying Fractions

Multiply top by top, bottom by bottom

Literal Equations

Solving for x -- isolate the x

First, undo the y by adding y on both sides

Multiplying Powers

Add the exponents, getting x⁵

Powers of Powers

Multiply the exponents

Dividing Powers

Divide the whole numbers, then cancel the exponents one at a time

15/5 becomes 3/1

x³/x becomes x²

Binomial Multiplication

Multiply each term separately, then add the result.

Solving Quadratics

Set each part equal to zero, then find what value of x makes that part equal zero.

3x=0 --> x=0

(x-7)=0 --> x=7

BOTH of these are your answer

Solving Quadratics

Set each part equal to zero, then find what value of x makes that part equal zero.

(x+4)=0 --> x=-4

(x-2)=0 --> x=2

BOTH of these are your answer

Factoring Quadratics

Find the two factors that, once multiplied, equal the quadratic.

Start with the x², then with the -21, then find the sign that makes the +4x work.

(x+7)(x-3)

Factoring Quadratics

First, factor out the 8 from all terms:

8x²+32x+32 becomes 8(x²+4x+4), which is easier

Your answer, after normal factoring, becomes 8(x+2)(x+2)

Dividing Quadratics Tricks

Factor the numerator, then divide by the denomenator.  Something should cancel out, making it easier!

Solving Difficult Problems

First, try factoring.  In this case, you can factor the top quadratic.  Then, divide by the bottom, and it's an easy problem!