Question

solve
|x - 7| = 28
x =
(simplify your answers. type an integer or a fraction. use commas to separate answers as needed.)

Explanation:

Step1: Recall absolute value definition

If \(|a| = b\) (\(b\geq0\)), then \(a = b\) or \(a=-b\). For \(|x - 7|=28\), we have two cases.

Step2: Solve case 1 (\(x - 7 = 28\))

Add 7 to both sides: \(x=28 + 7=35\).

Step3: Solve case 2 (\(x - 7=-28\))

Add 7 to both sides: \(x=-28 + 7=-21\).

Answer:

\(x = 35, -21\)