Question

select the correct answer. what is the solution to |2x + 3| = 15? a. x = 6 b. x = 6 or x = -6 c. x = 6 or x = -9 d. no solutions exist.

Explanation:

Step1: Recall absolute value definition

For \(|A| = B\) (\(B\geq0\)), \(A = B\) or \(A=-B\). So for \(|2x + 3| = 15\), we have two cases.

Step2: Solve Case 1: \(2x + 3 = 15\)

Subtract 3 from both sides: \(2x = 15 - 3 = 12\).
Divide by 2: \(x=\frac{12}{2}=6\).

Step3: Solve Case 2: \(2x + 3 = -15\)

Subtract 3 from both sides: \(2x = -15 - 3 = -18\).
Divide by 2: \(x=\frac{-18}{2}=-9\).

Answer:

C. \(x = 6\) or \(x = -9\)