Question

If \( |x + 3| < 2 \), then \( x \) lies in

• A. \( (-5, -1) \)
• B. \( (-2, 2) \)
• C. \( (-4, -2) \)
• D. (-1, 5)

Hint:

When solving absolute value inequalities, break them down into two separate inequalities and solve accordingly.

Answer 1

The Correct Option is A

The inequality given is \( |x + 3| < 2 \). This can be rewritten as: \[ -2 < x + 3 < 2 \] Now, subtract 3 from all parts of the inequality: \[ -5 < x < -1 \] Thus, the solution to the inequality is \( x \) lying in the interval \( (-5, -1) \). So, the correct answer is \( (-5, -1) \).