Question

find the real solutions of |8x + 7| = 7. select the correct choice below and fill in any answer boxes within your choice. a. the solution set is. (use a comma to separate answers as needed.) b. the solution set is all real numbers. c. the solution set is the empty set.

Explanation:

Step1: Apply absolute value definition

For \(|8x + 7| = 7\), we have two cases:
Case 1: \(8x + 7 = 7\)
Case 2: \(8x + 7 = -7\)

Step2: Solve Case 1

\(8x + 7 = 7\)
Subtract 7 from both sides: \(8x = 7 - 7 = 0\)
Divide by 8: \(x = \frac{0}{8} = 0\)

Step3: Solve Case 2

\(8x + 7 = -7\)
Subtract 7 from both sides: \(8x = -7 - 7 = -14\)
Divide by 8: \(x = \frac{-14}{8} = -\frac{7}{4}\)

Answer:

A. The solution set is \(0, -\frac{7}{4}\)