Question

solve the following absolute value equation.
$\frac{|x + 6|}{7} = 2$
$x = ?, $
enter the smallest solution first.

Explanation:

Step1: Eliminate denominator

Multiply both sides by 7:
$$|x+6| = 2 \times 7$$
$$|x+6| = 14$$

Step2: Split absolute value case 1

Set inside equal to 14:
$$x+6 = 14$$
$$x = 14 - 6$$
$$x = 8$$

Step3: Split absolute value case 2

Set inside equal to -14:
$$x+6 = -14$$
$$x = -14 - 6$$
$$x = -20$$

Step4: Order solutions from smallest

Compare -20 and 8: $-20 < 8$

Answer:

$x = -20, 8$