Algebra Unit Test 1

Order of Operations and Properties of Mathematics

100

8 + 9(6) - 4

58

200

(11 - 4 )( 8 - 3 ) + 7^2

(11 - 4 )( 8 - 3 ) + 7^2 --> (7)(5) + 7^2 --> 35 + 49 84

300

14 + 13 = 13 + 14 This is an example of __________________ property.

Commutative Property of Addition

400

(12*5) * 3 = 12 * (5 * 3) This is an example of __________________.

Associative Property of Multiplication

500

2(6 + 4) = 2(6) + 2(4)

Distributive Property

Distributive Property and collect like terms

100

5(x + 3)

5(x + 3) --> (5)(x) + (5)(3) distributive prop --> 5x + 15 simplify

200

-4(-1 - 4x)

-4(-1 - 4x) --> (-4)(-1) + (-4)(-4x) distributive prop --> 4 - 16x simplify

300

9x + 2 - 3x -16

9x + 2 - 3x -16 --> 9x - 3x + 2 - 16 commutative prop of addition --> 6x - 14 simplify

400

9(-3x-5) + 12

9(-3x-5) + 12 --> (9)(-3x) + (9)(-5) + 12 distributive prop --> -27x - 45 + 12 simplify --> -27x - 33 collect like terms

500

-2(6 - 7x) + 12x - 15

-2(6 - 7x) + 12x - 15 --> (-2)(6) + (-2)(-7x) + 12x - 15 distributive prop --> -12 + 14x + 12x - 15 simplify --> -12 - 15 + 14x + 12x comm. prop. of addition --> -27 + 26x collect like terms

Evaluate Expressions

100

7 - x where x = 2

7 - x where x = 2 --> 7 - 2 substitute --> 5 simplify

200

x / 10 where x = 90

x / 10 --> 90 / 10 substitute --> 9 simplify

400

10(-3 - 6x) where x = 2

10(-3 - 6x) --> 10[-3 - 6(2)] substitute --> 10[-3 - 12] simplify --> 10[-15] simplify --> -150

500

12x + 4(6 - 3x) where x =3

12x + 4(6 - 3x) where x =3 --> 12(3) + 4[6 - (3)(3)] substitute --> 36 + 4[6 - 9] simplify --> 36 + 4(-3) simplify --> 36 + (-12) simplify --> 24

Evaluate Equations

100

what are the two steps to evaluating?

substitute and simplify

200

12x = 60

12x = 60 --> 12x/12 = 60/12 inverse operations --> x = 5

300

3x - 15 = -39

3x - 15 = -39 --> 3x - 15 + 15 = -39 + 15 inverse operations --> 3x = -24 simplify --> 3x/3 = -24/3 inverse operations --> x = -8 simplify

400

2(x-5) + 7 = 53

2(x-5) + 7 = 53 --> 2(x) + 2(-5) + 7 = 53 --> 2x - 10 + 7 = 53 --> 2x - 3 = 53 --> 2x - 3 + 3 = 53 + 3 --> 2x = 56 --> 2x/2 = 56/2 --> x = 28

500

6 - 9x = -39

6 - 9x = -39 --> 6 - 9x - 6 = -39 - 6 inverse operations --> -9x = -45 simplify --> -9x/-9 = -45/-9 inverse operations --> x = 5 simplify

Translate Algebraic Expressions

100

the sum of x and 7

x + 7

200

Movie tickets are $6 each. Write an expression that represents this relationship between the cost of each ticket and x number of tickets.

6x

300

Chess club has 57 hotdogs at the beginning of the volleyball game and sold N hotdogs. How many hotdogs are left? Create an expression that represents this relationship

57 - N

400

concert tickets are $35 each plus a one time convenience charge of $4. let x represent the number of concert tickets. create an expression that represents this relationship

35x + 4

500

Cab fare in Farmington is $7.50 for the first mile plus $3 for each extra mile. let N represent the number of miles create an expression that represents this relationship

7.50 + 3n