Question

find the real solutions of the equation.
|7x + 8| = 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 \(|a| = b\) (\(b\geq0\)), \(a = b\) or \(a=-b\). So for \(|7x + 8| = 7\), we get two equations:
\(7x + 8 = 7\) or \(7x + 8=-7\)

Step2: Solve \(7x + 8 = 7\)

Subtract 8 from both sides: \(7x=7 - 8=-1\)
Divide by 7: \(x=\frac{-1}{7}\)

Step3: Solve \(7x + 8=-7\)

Subtract 8 from both sides: \(7x=-7 - 8=-15\)
Divide by 7: \(x=\frac{-15}{7}\)

Answer:

A. The solution set is \(-\frac{1}{7},-\frac{15}{7}\)