# Algebra 1 Companion Book, Vol 1 – Summer Edition

3.2.2 Solving Inequalities with Variables on Both Sides - Worksheet

Example 1:

Solve each inequality and graph the solutions.

1. 2 x > 4 x − 6

2. 7 y + 1 ≤ y − 5

3. 27 x + 33 > 58 x − 29

4. − 3 r < 10 − r

5. 5 c − 4 > 8 c + 2

6. 4.5 x − 3.8 ≥ 1.5 x − 2.3

Example 2:

7. The school band will sell pizzas to raise money for new uniforms. The supplier charges \$100 plus \$4 per pizza. If the band members sell the pizzas for \$7 each, how many pizzas will they have to sell to make a profit?

Example 3:

Solve each inequality and graph the solutions.

8. 5(4 + x ) ≤ 3(2 + x )

9. − 4(3 − p ) > 5( p + 1)

10. 2(6 − x ) < 4 x

1 3

1 6

3 4

1 4

11. 4 x > 3(7 − x )

12.

13. − 36.72 + 1.8 t + 3.85 t < 0.25 t

+ + ≥ f f f

Example 4: Solve each inequality. 14. 2( x − 2) ≤ − 2(1 − x )

15. 4( y + 1) < 4 y + 2

16. 4 v + 1 < 4 v − 7

17. b − 4 ≥ b − 6

18. 3( x − 5) > 3 x

19. 2 k + 7 ≥ 2( k + 14)

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