Which of the following is the solution set of | 2x – 3 | > 4?

Answer 1

2x-3 = 4

2x =7

x =7/2 = 3.5 is a dividing line of the solution interval

-2x +3 = 4

2x = -1

x =-1/2 is the other dividing line

x>3.5 and x< -0.5

the solution intervals are (-infinity,-0.5) U (3.5,infinity)

Answer 2

Solution to the inequality |k| > a is given by solving the two inequalities:

k > a and k < -a

In this case, the inequality |2x - 3| > 4 is obtained by 2x - 3 > 4 and 2x - 3 < -4

2x - 3 > 4

2x > 4+3

2x > 7

x > 7/2

Consider the second inequality:

2x - 3 < -4

2x < -4+3

2x < -1

x < -1/2

Therefore, solution set is (-∞, -1/2) U (7/2, ∞).