Question

question 3. solve: |-3x - 4| = 2 a. x = -2 b. x = -2 or x = -2/3 c. x = 2/3 d. x = 2 or x = 2/3

Explanation:

Step1: Recall absolute value definition

For \(|A| = B\) (\(B\geq0\)), \(A = B\) or \(A=-B\). So for \(|-3x - 4| = 2\), we have two cases: \(-3x - 4 = 2\) or \(-3x - 4=-2\).

Step2: Solve first case (\(-3x - 4 = 2\))

Add 4 to both sides: \(-3x=2 + 4=6\).
Divide by \(-3\): \(x=\frac{6}{-3}=-2\).

Step3: Solve second case (\(-3x - 4=-2\))

Add 4 to both sides: \(-3x=-2 + 4 = 2\).
Divide by \(-3\): \(x=\frac{2}{-3}=-\frac{2}{3}\).

Answer:

B. \(x = -2\) or \(x = -\frac{2}{3}\)