Question

which of the following is(are) the solution(s) to |x - 1| = 8?

a. x = -7, 9
b. x = 7
c. x = 9
d. x = 7, -9

Explanation:

Step1: Recall absolute value definition

The equation \(|a| = b\) (where \(b\geq0\)) implies \(a = b\) or \(a=-b\). For \(|x - 1|=8\), we have two cases.

Step2: Solve Case 1: \(x - 1 = 8\)

Add 1 to both sides: \(x=8 + 1=9\).

Step3: Solve Case 2: \(x - 1=-8\)

Add 1 to both sides: \(x=-8 + 1=-7\).
So the solutions are \(x = -7\) and \(x = 9\).

Answer:

A. \(x=-7,9\)