Term- number or product of a number and a variable

Constant- term with no variable

Coefficient- number that multiplies to a variable

Like Terms- identical variables

Simplifying expressions- replacing with equivalent expression that has as few terms as possible

Ex: 2x + 4 + 3x = 5x + 4 Ex: 3a + 2 + 4a - 1 = 7a + 1

Equations – math sentence with an equal sign

Open sentence – equation with one or more variables

You can check an equation by substituting your answer back into the equation

Ex: 170 + x = 200, is the solution 30?

170 + (30) = 200, yes

Ex: 8 + r = 2r, is the solution 1? 8 + 1 = 2 * 1 9 ≠ 2, no

Remember the Integer Rules:Same signs addTwo negatives together becomes a

positive Ex: 5 – (-3) = 8

Different signs subtract Keep the sign of the larger number

Do the inverse operations

Ex: x + 6 = 4 -6 -6 X = -2

Ex: a + 8 = 3-8 = -8 a = -5

C + (-4) = -5 +4 = +4 c = -1

Remember the Integer Rules:Positive times Positive = PositivePositive times Negative =

NegativeNegative times Negative =

Positive

The same rules apply for dividing!!

Do the inverse operation

Ex: 4x = 84 4 4 x = 21

Ex: -3b = 24 -3 -3 b = -8

Ex: x = -3 -9 (-9) x = -3 (-9) 1 -9 x = 27

Ex: a = 54 6 (6) a = 54 (6) 1 6 a = 324

Inequality is a math sentence that contains:

<, >, ≤ , ≥ , = , ≠

Closed dot shown the # is a solution Ex: x ≥ -2

-3 -2 -1 0 1 2 3

Open dot shows that the # isn’t a solution

Ex: x < 2

-4 -3 -2 -1 0 1 2 3 4

Solving inequalities is the same as solving equations

Don’t forget the integer rules!!

Do the inverse operation

Addition and Subtraction

Rules for Adding/Subtracting:Same signs addDifferent signs subtract

(keep sign of larger #)

M – 13 > 29 +13 +13

M > 42

N + 8 ≥ 19 -8 -8 N ≥ 11

Multiplication and Division

Rules for Multiplying/Dividing with Integers:Negative x negative = positivePositive x negative = negativeSame for dividing

New Rules for Multiplying and Dividing Inequalites: Multiply or divide each side of the

inequality by a POSITIVE number leave the symbol unchanged

Multiply or divide each side of the inequality by a NEGATIVE number then symbol reverses

4x > 40 (divide to solve) 4 4 X > 10 (sign stays unchanged)

T ≤ 7 (multiply to solve) -4

(-4) T≤ 7 (-4) 1 -4 1 T ≥ -28 (sign reverses)