Solve each inequality. Give the solution set in both interval.?

Question

1. -1/4 (p + 6) + 3/2 (2p - 5) < 10
2. 3 (2x - 4) -4x < 2x + 3
3. 8 (1/2x + 3) < 8 (1/2x - 1)

Answer 1

1. -1/4 (p + 6) + 3/2 (2p - 5) < 10

a.) Multiply out the terms:
-1/4p - 3/2 + 3p - 15/2 < 10

b.) Combine like terms:
11/4p - 9 < 10

c.) Move the 9 to the other side:
11/4p < 19

d.) Divide both sides by 4/11:
p < 76/11
p < 6 10/11

2. 3 (2x - 4) -4x < 2x + 3

a.) Multiply out the terms:
6x - 12 - 4x < 2x + 3

b.) Combine like terms:
2x - 12 < 2x + 3

c.) Subtract 2x + 3 from both sides:
2x - 12 - 2x - 3 < 0

d.) Combine like terms:
9 < 0

Solution: All values of x, because 9 is always greater than 0.

3. 8 (1/2x + 3) < 8 (1/2x - 1)
a.) Multiply out the terms:
4x + 24 < 4x - 8

b.) Subtract 4x -8 from both sides:
4x + 24 - 4x + 8 < 0

c.) Combine like terms:
30 < 0

Solution: All values of x, because 30 is always greater than 0.