Question

C. Solve and graph the following.

1.) |2x + 3| < 5
2.) |4x - 7| < 2​

Answer 1

1)
-4 < x < 1

2)
5/4 < x < 9/4

or In decimal:

1.25 < x < 2.25

Explanation:

For both parts apply the absolute rule of inequality which states:
if |u| < a, and a > 0 then -a < u < a

For 1) |2x + 3| < 5

Substitute u = 2x + 3, a = 5

This gives
-5 < 2x + 3 < 5

Subtract 3 all sides

-5 - 3 < 2x < 5 - 3
-8 < 2x < 2

Divide throughout by 2:
-8/2 < 2x/2 < 2/2
==> -4 < x < 1

For 2) |4x - 7| < 2​

Substituting u = 4x - 7 and a = 2:
-2 < 4x - 7 < 2
-2 + 7 < 4x < 2 + 7

5 < 4x < 9

5/4 < x < 9/4

In decimal:
1.25 < x < 2.25