Question

Johan found that the equation –2|8 – x| – 6 = –12 had two possible solutions: x = 5 and x = –11. Which explains whether his solutions are correct?

He is correct because both solutions satisfy the equation.
He is not correct because he made a sign error.
He is not correct because there are no solutions.
He is not correct because there is only one solution: x = 5.

Answer 1

He is not correct because he made a sign error.

Work: -2|8 − x| − 6 = −12 ⇒ −2|8 − x| = −6 ⇒ |8 − x| = 3.
So 8 − x = 3 ⇒ x = 5, or 8 − x = −3 ⇒ x = 11. Johan’s second solution should be 11, not −11.