Question

select the correct answer. what is the solution to \\( |2x + 3| < 7 \\)? \\( \bigcirc \\ x > 5 \text{ or } x < -2 \\) \\( \bigcirc \\ -5 < x < 2 \\) \\( \bigcirc \\ -2 < x < -5 \\) \\( \bigcirc \\ x > 2 \text{ or } x < -5 \\)

Explanation:

Step1: Rewrite absolute value inequality

For $|A| < B$ (where $B>0$), this is equivalent to $-B < A < B$. So:
$$-7 < 2x + 3 < 7$$

Step2: Subtract 3 from all parts

Isolate the term with $x$ by subtracting 3 from each segment of the inequality:
$$-7 - 3 < 2x + 3 - 3 < 7 - 3$$
$$-10 < 2x < 4$$

Step3: Divide all parts by 2

Solve for $x$ by dividing each segment by 2:
$$\frac{-10}{2} < \frac{2x}{2} < \frac{4}{2}$$
$$-5 < x < 2$$

Answer:

-5 < x < 2