Question

Which compound inequality is equivalent to the absolute value inequality ∣<3∣x∣<3?

A) −3B) −3≤x<3
C) −3D) −3≤x≤3

Answer 1

The compound inequality equivalent to the absolute value inequality |3|x|3 is -3 ≤ x < 3.

Step-by-step explanation:

The compound inequality equivalent to the absolute value inequality |3|x|3 is -3 ≤ x < 3. To understand why, let's break it down step by step:

1. The absolute value of any number is always non-negative, meaning it is greater than or equal to zero.
2. Since |3| is equal to 3, the inequality becomes 3|x|3.
3. Now, we need to find the values of x that satisfy this inequality. We can break it down further into two inequalities: -3 ≤ 3x and 3x < 3.
4. Simplifying each inequality, we get -1 ≤ x and x < 1.
5. Combining these two inequalities, we get -3 ≤ x < 3, which is the compound inequality equivalent to the given absolute value inequality.