Question

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

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 \(x=-4\) (corresponding to the option "x = 5 and x = - 4")