What does it mean if |2x – 3| < 7? It means that if the expression between the
absolute value bars is positive, it’s less than +7 or, if the expression between
the bars is negative, it’s greater than –7. In other words, 2 x – 3 is between –7
and +7:
The answer is (C).
In fact, there’s a general rule that applies here: To solve an inequality in the
form |whatever| < p, where p > 0, just put that “whatever” inside the range –p
to p:
|whatever| < p means: –p < whatever < pFor example, |x – 5| < 14 becomes –14 < x – 5 < 14.
1. Which of the following is the solution set of |2x – 3|< 7?(A) {x: –5 < x < 2}
(B) {x: –5 < x < 5}
(C) {x: –2 < x < 5}
(D) {x: x < –5 or x > 2}
(E) {x: x < –2 or x > 5}