Question

solve for all values of ( x ) in simplest form. ( |x + 7| + 1 = 3 ) answer attempt 1 out of 2 ( oplus ) additional solution ( ominus ) no solution ( x = )

Explanation:

Step1: Isolate the absolute value

Subtract 1 from both sides of the equation \(|x + 7| + 1 = 3\) to get \(|x + 7| = 3 - 1\).
\(|x + 7| = 2\)

Step2: Solve the absolute value equation

The absolute value equation \(|x + 7| = 2\) means that \(x + 7 = 2\) or \(x + 7 = -2\).

For \(x + 7 = 2\):

Subtract 7 from both sides: \(x = 2 - 7\)
\(x = -5\)

For \(x + 7 = -2\):

Subtract 7 from both sides: \(x = -2 - 7\)
\(x = -9\)

Answer:

\(x = -5\) or \(x = -9\)