Question

select the correct answer.

what is the solution to \\(|2x + 3| < 7\\)?

\\(x > 2\\) or \\(x < -5\\)

\\(-5 < x < 2\\)

\\(-2 < x < -5\\)

\\(x > 5\\) or \\(x < -2\\)

Explanation:

Set up the compound inequality

To solve the absolute value inequality \(|2x + 3| < 7\), we rewrite it as a compound inequality.

$$ -7 < 2x + 3 < 7 $$

Subtract 3 from all parts

Subtract 3 from each part of the compound inequality to isolate the variable term.

$$ -7 - 3 < 2x < 7 - 3 $$

$$ -10 < 2x < 4 $$

Divide all parts by 2

Divide each part by 2 to solve for \(x\).

$$ \frac{-10}{2} < x < \frac{4}{2} $$

$$ -5 < x < 2 $$

Answer:

• (A) \(x > 2\) or \(x < -5\)
• (B) \(-5 < x < 2\) (Correct answer)
• (C) \(-2 < x < -5\)
• (D) \(x > 5\) or \(x < -2\)