Question

Solve |x — 6| = 8.

X
OA.
A. x 14 and x = -2
X=
OB. x = -14 and x = 2
OC. x =
14 and x = -14
D. x =
-14 and x = -2

Answer 1

Answer: A. x = 14, x = -2

Explanation:

|x-6| = 8

this means x = 6+8 and x = 6-8

therefore, x = 14, x = -2

Answer 2

Answer: Choice A

x = 14 and x = -2

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Work Shown:

`|x-6| = 8\\\\x-6 = 8 \ \text{ or } \ x-6 = -8\\\\x = 8+6 \ \text{ or } \ x = -8+6\\\\x = 14 \ \text{ or } \ x = -2\\\\`

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Checking the answer x = 14

`|x-6| = 8\\\\|14-6| = 8\\\\|8| = 8\\\\8 = 8\\\\`

That solution is confirmed.

Repeat for x = -2

`|x-6| = 8\\\\|-2-6| = 8\\\\|-8| = 8\\\\8 = 8\\\\`

The second solution is confirmed.