Directions: Solve each problem using the correct algebraic rules. 1. Write an expression for each of the following:

a. the sum of 9 and z

b. the difference between 22 and x

c. 8 less than the quotient of x divided by 7

d. x increased by 10 divided by 4

2. Simplify:

a. 5x + 3x

b. 9s - 3s + 4s

c. 10t – 6t

d. 8xy + 3xy + x

e. (9x)2

f. 6x
xx2x

3. Add or subtract the following terms:

a. (11x) + (22x) =

b. (-6x) - (-6x) =

c. (-13t) + (14x) - (+13t) =

d. (-4t) + (+4t) - (-6t) =

4. Multiply the following signed numbers:

a. (-42x)(+2x) =

b. (+7x)(-4x)(-3x) =

c. (+7)(-4)(-4) =

d. (+10)(-2)(-2)(+4) =

5. Divide the following signed numbers:

a.

-8
-2

b.

+9

-1

c.

-12

-48

6. Solve the following equations:

a. x + 8 = 28

b. y - 4 = 30

c. s + 2s = 36

d. t - t + 4t = 16

e. 5a = 15

f. 8x - x = 21

7. Add or subtract the following polynomials:

a. 5x2 + 3y3 - 4x2 =

b. y3 + 2y3 - 8 + 2 =

c. 9 - 3x - 4x + 2x - 12 =

d. -6t + 4t2 - 6 + 7t - 4t2 =

8. Multiply the following:

a. (x3)(x2) =

b. (x7)(x10) =

c. (3s4)(-6s5) =

d. (-20x)(3x) =

9. Divide the following:

a.

x4
x3

b.

s3

s5

c.

z12

z10

10. Remove the parentheses by multiplication:

a. 6(2a - 4) =

b. x(2x + 10) =

c. 5(9x - 9) =

d. 3x(2x - x) =

11. Solve the following equations:

a. 5(x - 4) = 10

b. 2x(4x + 3x) = 21

c. 3(4 - 2x) = 28

d. 10x(2 + 13) = 300

12. Multiply the following binomials:

a. (x + 3)(x - 4)

b. (s - 2)(2s - 12)

c. (4s - 12)(2s + 4)

d. (2x - 4)(2x - 4)

13. Solve the following inequalities:

a. 3x - 3 > 6

b. 24x + 4 < 52

c. -2x - 2 < 8

d. 10x - 100 > 0

14. Factor the following:

a. x2 - 25

b. y2 - 36

c. x2 - 14x + 13

d. s2 + 7s + 10

e. q2 - 7q + 12

f. r2 + 13r + 12

g. x2 - x - 20

h. y2 + 5y + 6

i. b2 + b - 12

j. k2 - 5k + 6