3(9z + 4) > 35z – 4 Original problem. Solve each inequality. Then graph the solution set on the number line. 3(9z + 4) > 35z – 4 Original problem. 3(9z + 4) > 35z – 4 Rewrite the problem. 27z + 12 > 35z – 4 Distributive Property. -8z + 12 > -4 Move 35z to other side. -8z > -16 Move 12 to other side. z < 2 Move -8. Must flip inequality. The Solution Set is {z | z < 2}. Now graph the solution.

4. 18 – 4k < 2(k + 21) Original problem. Solve each inequality. Then graph the solution set on the number line. 4. 18 – 4k < 2(k + 21) Original problem. 18 – 4k < 2(k + 21) Rewrite the problem. 18 – 4k < 2k + 42 Distributive Property. 18 – 6k < 42 Move 2k to other side. -6k < 24 Move 18 to other side. k > -4 Move -6. Must flip inequality. The Solution Set is {k | k > -4}. Now graph the solution.

6. 2 + 3(m + 5) ≥ 4(m + 3) Original problem. Solve each inequality. Then graph the solution set on the number line. 6. 2 + 3(m + 5) ≥ 4(m + 3) Original problem. 2 + 3(m + 5) ≥ 4(m + 3) Rewrite the problem. 2 + 3m + 15 ≥ 4m + 12 Distributive Property two times. -1m + 17 ≥ 12 Move 4m and combine like terms. -1m ≥ -5 Move 17 to other side. m ≤ 5 Move -1. Must flip inequality. The Solution Set is {m | m ≤ 5}. Now graph the solution.

8. (1/3)(2y – 3) > y + 2 Original problem. Solve each inequality. Then graph the solution set on the number line. 8. (1/3)(2y – 3) > y + 2 Original problem. (1/3)(2y – 3) > y + 2 Rewrite the problem. (2/3)y – 1 > 1y + 2 Distributive Property. (-1/3)y – 1 > 2 Move 1y to other side. (-1/3)y > 3 Move -1 to other side. y < -9 Move -1/3. Must flip inequality. The Solution Set is {y | y < -9}. Now graph the solution.

1. c ≥ (c + 4)/3 Original problem. c ≥ (c + 4)/3 Rewrite the problem. Solve each inequality. Then graph the solution set on the number line. 1. c ≥ (c + 4)/3 Original problem. c ≥ (c + 4)/3 Rewrite the problem. 3c ≥ 1c + 4 Multiply the equation by 3. 2c ≥ 4 Move 1c to other side. c ≥ 2 Move 2 to other side. The Solution Set is {c | c ≥ 2}. Now graph the solution.

1. 3h < (2h + 26)/5 Original problem. Solve each inequality. Then graph the solution set on the number line. 1. 3h < (2h + 26)/5 Original problem. 3h < (2h + 26)/5 Rewrite the problem. 15h < 2h + 26 Multiply the equation by 5. 13h < 26 Move 2h to other side. h < 2 Move 13 to other side. The Solution Set is {h | h < 2}. Now graph the solution.

5.75h – 0.26(5.75h) ≥ 110 5.75h – 1.494h ≥ 110 4.255h ≥ 110 h ≥ 25.85194 Final Answer is 26 hours or more.