Question

. Below are the steps to solve an equation:
Step 1: |x - 4| + 1 = 8

Step 2: |x - 4| = 8 - 1

Step 3: |x - 4| = 7

Which of the following is a correct next step to solve the equation? (4 points)


x - 4 = -7
x + 4 = -7
-x - 4 = 7
x + 4 = 7

Answer 1

\(\bf |x - 4| = 7\implies
\begin{cases}
+(x - 4) = 7\implies x-4=7\\ \quad \\
\bf -(x - 4) = 7\implies x-4=-7
\end{cases}\)

Answer 2

absolute value equations have 2 cases or scenarios, and thus "x" will have 2 values, one for each scenario