Question

now find: solve the following absolute value equation: |x - 4| + 3 = 8

Explanation:

Step1: Isolate the absolute value

Subtract 3 from both sides of the equation \(|x - 4| + 3 = 8\).
\(|x - 4| + 3 - 3 = 8 - 3\)
\(|x - 4| = 5\)

Step2: Solve the absolute value equation

The absolute value equation \(|x - 4| = 5\) means that \(x - 4 = 5\) or \(x - 4 = -5\) (because if \(|a| = b\) where \(b\geq0\), then \(a = b\) or \(a = -b\)).

For \(x - 4 = 5\):

Add 4 to both sides:
\(x - 4 + 4 = 5 + 4\)
\(x = 9\)

For \(x - 4 = -5\):

Add 4 to both sides:
\(x - 4 + 4 = -5 + 4\)
\(x = -1\)

Answer:

The solutions are \(x = 9\) and \(x = -1\)