5. 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 > 35z – 4 Distributive Property.
-8z > Move 35z to other side.
-8z > Move 12 to other side.
z < Move -8. Must flip inequality.
The Solution Set is {z | z < 2}. Now graph the solution.

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

7. 6. 2 + 3(m + 5) ≥ 4(m + 3) Original problem.
Solve each inequality. Then graph the solution set on the number line.
(m + 5) ≥ 4(m + 3) Original problem.
2 + 3(m + 5) ≥ 4(m + 3) Rewrite the problem.
2 + 3m ≥ 4m Distributive Property two times.
-1m ≥ Move 4m and combine like terms.
-1m ≥ Move 17 to other side.
m ≤ Move -1. Must flip inequality.
The Solution Set is {m | m ≤ 5}. Now graph the solution.

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

9. 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 Multiply the equation by 3.
2c ≥ Move 1c to other side.
c ≥ Move 2 to other side.
The Solution Set is {c | c ≥ 2}. Now graph the solution.

10. 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 Multiply the equation by 5.
13h < Move 2h to other side.
h < Move 13 to other side.
The Solution Set is {h | h < 2}. Now graph the solution.

12. 5.75h – 0.26(5.75h) ≥ 110
5.75h – 1.494h ≥ 110
4.255h ≥ 110
h ≥
Final Answer is 26 hours or more.