Question

if $|7x + 12| = 2$, which statement is correct?
a $x = \frac{10}{7}$ or $x = \frac{10}{7}$
b $x = 2$ or $x = \frac{10}{7}$
c $x = -2$ or $x = \frac{10}{7}$
d $x = 2$ or $x = \frac{-10}{7}$
e $x = -2$ or $x = \frac{-10}{7}$

Explanation:

Step1: Split absolute value equation

For $|7x + 12| = 2$, we get two cases:
$7x + 12 = 2$ or $7x + 12 = -2$

Step2: Solve first linear equation

Isolate $x$ by subtracting 12:
$7x = 2 - 12$
$7x = -10$
Divide by 7:
$x = \frac{-10}{7}$

Step3: Solve second linear equation

Isolate $x$ by subtracting 12:
$7x = -2 - 12$
$7x = -14$
Divide by 7:
$x = -2$

Answer:

E. $x = -2$ or $x = \frac{-10}{7}$