Review

Definitions

100

any quantity that can change

variable

200

7x; 7 is a _______ and it means x + x + x + x + x + x + x

coefficent

300

single number or variable, or numbers and variables multiplied together

term

400

whole numbers that are positive or negative

integer

500

Parentheses Exponents Multiplication/Division Addition/Subtraction

Order of Operations

Properties

100

5 + 7 + 9 = 9 + 7 + 5

Commutative Property of Addition

200

(-3 + 12) + 72 = -3 + (12 + 72)

Associative Property of Addition

300

(-9)(-4) = (-4)(-9)

Commutative Property of Multiplication

400

4 * 7 * -3 = -3 * 4 * 7

Commutative Property of Multiplication

500

-6(3 + 5x)

Distributive Property

Simplifying

100

3(1 + 5x)

(3)(1) + (3)(5x) 3 + 15x

200

-7(-4x - 10)

(-7)(-4x) + (-7)(-10) 28x + 70

300

12x + 4 - 7x + 15

(12x - 7x) + (4 + 15) 5x + 19

400

-4x + 8(2x - 3)

8(2x - 3) - 4x Commutative Prop. of Addition (8)(2x) + (8)(-3) - 4x 16x - 24 - 4x 12x - 24

500

-3(5 + 2x) - 7

(-3)(5) + (-3)(2x) - 7 -15 + (-6x) - 7 -22 - 6x

Translating

100

9 less than a number

x - 9

200

6 more than 2 times a number

2x + 6

300

8 less than a number; multiply the result by 5

5(x-8)

400

8 less than a number; divide the result by 3

(x-8) / 3

500

A number multiplied by itself multiplied by itself

x^3

Evaluating

100

x - 7 where x = 16

16 - 7 9

200

4v – 3 at v = –5

4(-5) - 3 -20 - 3 -23

300

z(z – 7) at z = 5

5(5 - 7) 5(-2) -10

400

(n)^2 – 9n – 11 at n = 7

(7)^2 – 9(7) – 11 49 - 63 - 11 -25

500

(q)^3 – 3q + 12 at q = –5

(-5)^3 – 3(-5) + 12 -125 + 15 + 12 -98