Find the solution set for the inequality. -|x| 1 and x

Question

Find the solution set for the inequality. -|x| < 1 A) {x|x < -1 or x > 1} B) {x|x > 1 and x < -1} D) {x|-1 < x < 1}

Quizplus · Accepted Answer

The inequality |x| < 1 means that x can be any value between -1 and 1, but not including -1 or 1. Therefore, the solution set is {x|-1 < x < 1}. Option (A) includes values outside of this range, option (B) is a contradictory statement, and option (C) is not a valid choice as it is not one of the given options. Thus, option (D) is the best choice. When you have an inequality involving absolute value, you can approach it by separating it into two separate inequalities.
For |x| < 1:
The first inequality is x < 1
The second inequality is x > -1
When we look at the two inequalities together, the only solution is when -1 < x < 1. Therefore, the answer is D.

Find the Solution Set for the Inequality