Question

solve the following absolute value equation.
$\frac{|3x - 3|}{5} = 6$
$x = ?, $
enter the smallest solution first.

Explanation:

Step1: Eliminate denominator

Multiply both sides by 5:
$$|3x - 3| = 6 \times 5$$
$$|3x - 3| = 30$$

Step2: Split absolute value case1

Set inside equal to positive value:
$$3x - 3 = 30$$
Add 3 to both sides:
$$3x = 33$$
Divide by 3:
$$x = 11$$

Step3: Split absolute value case2

Set inside equal to negative value:
$$3x - 3 = -30$$
Add 3 to both sides:
$$3x = -27$$
Divide by 3:
$$x = -9$$

Step4: Order solutions

Compare -9 and 11, smallest first.

Answer:

$x = -9, 11$