Question

solve
|x - 5| - 12 = -6
a. {-11, 11}
b. {-1, 11}
c. {1, 11}
d. {-11, 1}

Explanation:

Step1: Isolate the absolute value expression

Add 12 to both sides of the equation \(|x - 5| - 12=-6\).
We get \(|x - 5|=-6 + 12\), which simplifies to \(|x - 5| = 6\).

Step2: Solve the absolute value equation

The absolute value equation \(|x - 5| = 6\) means that \(x-5 = 6\) or \(x - 5=-6\).

• For \(x-5 = 6\), add 5 to both sides: \(x=6 + 5=11\).
• For \(x - 5=-6\), add 5 to both sides: \(x=-6 + 5=-1\).

Answer:

B. \(\{-1, 11\}\)