Huether's Chapter 7 Pre-Algebra Test

Variables on Both Sides

100

5x = 28 - 2x

x = 4

200

7b - 20 = 8b

b = -20

300

5(x - 6) = 3x

x = 15

400

13g - 9 = 2(g - 8)

g = -7/11

500

7(a + 3) + a = 5(a + 6) + 9

a = 6

Solving Inequalities

100

4y + 3 < 15

y < 3

200

-33x + 37 > 70

x < -1

300

7 - 2y ≥ 16

y ≥ -4.5

400

3(w - 4) > 2w + 1

w > 13

500

4(y - 9) < y + 3

y < 13

Identities & Contradictions

100

x + 3 = 3

one sol; x = 0

200

-2r = 4r - 6r

Identity; -2r = -2r

300

7x + 14 = 7x - 14

No solution; 14 = -14

400

12x = 6(2x - 1)

No solution; 0 = -6

500

3(2m - 5) = 2m - 15 + 4m

Identity; -15 = -15

Solving Equations with Powers

100

x³ = -64

x = -4

200

3x² = 75

x = 5, -5

300

2x³ = 250

x = 5

400

x² + 6 = 2x² − 30

x = 6, -6

500

3(x - 2)² = 75

7, -3

Radical Equations

100

√4

x = 16

200

5√d = -30

No Solution

300

∛y-2 = -3

y = -25

400

√a + 6  + 4 = 9

a = 19

500

∛y + 2  - 2 = 5

y = 341