Question

7 solve the equation: |b + 1| = 4
a. 24 and -24
b. 24
c. -2 and 2
d. 3 and -5

Explanation:

Step1: Recall absolute value definition

The absolute value equation \(|x| = a\) (where \(a\geq0\)) has solutions \(x = a\) or \(x=-a\). For \(|b + 1|=4\), we set up two cases.

Step2: Case 1: \(b + 1 = 4\)

Solve for \(b\) by subtracting 1 from both sides:
\(b=4 - 1=3\)

Step3: Case 2: \(b + 1=-4\)

Solve for \(b\) by subtracting 1 from both sides:
\(b=-4 - 1=-5\)

Answer:

D. 3 and -5