Question

solve for x |2x - 1| = 9. options: no solution; x = 5 and x = -4; x = 5 and x = -5; only x = 5

Explanation:

Step1: Recall absolute value definition

For \(|a| = b\) (\(b\geq0\)), \(a = b\) or \(a=-b\). So for \(|2x - 1|=9\), we have two cases:
Case 1: \(2x - 1 = 9\)
Case 2: \(2x - 1=-9\)

Step2: Solve Case 1

Solve \(2x - 1 = 9\). Add 1 to both sides: \(2x=9 + 1=10\). Divide by 2: \(x=\frac{10}{2}=5\).

Step3: Solve Case 2

Solve \(2x - 1=-9\). Add 1 to both sides: \(2x=-9 + 1=-8\). Divide by 2: \(x=\frac{-8}{2}=-4\).

Answer:

x = 5 and x = -4