Question

solve the equation.
5|x - 3| - 2 = 18
x = ? or x =
enter the smaller solution first.

Explanation:

Step1: Isolate the absolute value term

Add 2 to both sides of the equation \(5|x - 3| - 2 = 18\).
\(5|x - 3| - 2 + 2 = 18 + 2\)
\(5|x - 3| = 20\)

Step2: Solve for the absolute value

Divide both sides by 5.
\(\frac{5|x - 3|}{5} = \frac{20}{5}\)
\(|x - 3| = 4\)

Step3: Solve the two cases for the absolute value

Case 1: \(x - 3 = 4\)
Add 3 to both sides: \(x - 3 + 3 = 4 + 3\)
\(x = 7\)

Case 2: \(x - 3 = -4\)
Add 3 to both sides: \(x - 3 + 3 = -4 + 3\)
\(x = -1\)

Answer:

\(x = -1\) or \(x = 7\)