Question

solve $|x - 6| = 8$
a. $x = -14$ and $x = 2$
b. $x = -14$ and $x = -2$
c. $x = 14$ and $x = -14$
d. $x = 14$ and $x = -2$

Explanation:

Step1: Split absolute value equation

For $|x-6|=8$, we have two cases:
Case 1: $x-6=8$
Case 2: $x-6=-8$

Step2: Solve Case 1

Isolate $x$ by adding 6 to both sides.
$x = 8 + 6 = 14$

Step3: Solve Case 2

Isolate $x$ by adding 6 to both sides.
$x = -8 + 6 = -2$

Answer:

D. $x = 14$ and $x = -2$