Question

solve the following equation. if there are multiple answers, enter each answer separated by a comma. enter none if there are no solutions.\\(|x + 3| = 8\\)\\(x =\\)

Explanation:

Step1: Recall absolute value definition

The absolute value equation \(|A| = B\) (where \(B\geq0\)) is equivalent to \(A = B\) or \(A=-B\). For \(|x + 3|=8\), we set up two equations:
\(x + 3=8\) or \(x + 3=-8\)

Step2: Solve \(x + 3=8\)

Subtract 3 from both sides:
\(x=8 - 3\)
\(x = 5\)

Step3: Solve \(x + 3=-8\)

Subtract 3 from both sides:
\(x=-8 - 3\)
\(x=-11\)

Answer:

5, -11