Question

28)
an equation is shown.

$6|x - 10| - 54 = 0$

select all of the solutions to the equation.

Explanation:

Step1: Isolate the absolute value term

Add 54 to both sides of the equation \(6|x - 10| - 54 = 0\):
\(6|x - 10| = 54\)
Then divide both sides by 6:
\(|x - 10| = \frac{54}{6} = 9\)

Step2: Solve the absolute value equation

The absolute value equation \(|x - 10| = 9\) means that \(x - 10 = 9\) or \(x - 10 = -9\)
For \(x - 10 = 9\), add 10 to both sides:
\(x = 9 + 10 = 19\)
For \(x - 10 = -9\), add 10 to both sides:
\(x = -9 + 10 = 1\)

Answer:

The solutions to the equation are \(x = 1\) and \(x = 19\)