Question

solve |x - 2| + 5 = 9. the solutions are x = \square and x = \square.

Explanation:

Step1: Isolate the absolute value

Subtract 5 from both sides of the equation \(|x - 2| + 5 = 9\) to get \(|x - 2| = 9 - 5\).
\(|x - 2| = 4\)

Step2: Solve the absolute value equation

The absolute value equation \(|x - 2| = 4\) means that \(x - 2 = 4\) or \(x - 2 = -4\).

For \(x - 2 = 4\):

Add 2 to both sides: \(x = 4 + 2\)
\(x = 6\)

For \(x - 2 = -4\):

Add 2 to both sides: \(x = -4 + 2\)
\(x = -2\)

Answer:

The solutions are \(x = 6\) and \(x = -2\).