Question

Solve the absolute value inequality: |2x - 3| < 7

Answer 1

The most formal way to do this is to divide the real numbers.

For 2x - 3 >= 0, the absolute values do nothing. Get rid of them.

2x - 3 < 7 GIVEN THAT 2x - 3 >= 0 or x >= 3/2.

For 2x - 3 < 0, the absolute values change the sign of the argument.

-(2x - 3) < 7 GIVEN THAT 2x - 3 < 0 or x < 3/2.

Solve both! Keep in mind that each solution has TWO parts.