Question

1. solve the equation: |8a - 7| + 4 = 13

a. -1 and -11
b. -1
c. 2 and -\frac{1}{4}
d. 2

Explanation:

Step1: Isolate the absolute value

Subtract 4 from both sides of the equation \(|8a - 7| + 4 = 13\) to get \(|8a - 7| = 13 - 4\).
\(|8a - 7| = 9\)

Step2: Solve the two cases

Case 1: \(8a - 7 = 9\)
Add 7 to both sides: \(8a = 9 + 7\)
\(8a = 16\)
Divide by 8: \(a = \frac{16}{8} = 2\)

Case 2: \(8a - 7 = -9\)
Add 7 to both sides: \(8a = -9 + 7\)
\(8a = -2\)
Divide by 8: \(a = \frac{-2}{8} = -\frac{1}{4}\)

Answer:

C. 2 and \(-\frac{1}{4}\)