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.

Please answer with letters

Answer 1

To determine if Johan's solutions \( x = 5 \) and \( x = -11 \) are correct, we can check if they satisfy the original equation \(-2|8 - x| - 6 = -12\).

1. For \( x = 5 \):
\[
|8 - 5| = |3| = 3
\]
Substitute into the equation:
\[
-2(3) - 6 = -6 - 6 = -12
\]
This is correct.

2. For \( x = -11 \):
\[
|8 - (-11)| = |8 + 11| = |19| = 19
\]
Substitute into the equation:
\[
-2(19) - 6 = -38 - 6 = -44 \quad (\text{not equal to } -12)
\]
This is incorrect.

Since \( x = 5 \) is a solution but \( x = -11 \) is not, Johan is not correct because there is only one solution: \( x = 5 \).

The answer is: **D**.