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: $x = 5$.

Explanation:

Step1: Check \( x = 5 \)

Substitute \( x = 5 \) into \( -2|8 - x| - 6 \):
\( -2|8 - 5| - 6 = -2|3| - 6 = -2(3) - 6 = -6 - 6 = -12 \), which matches the right - hand side.

Step2: Check \( x=-11 \)

Substitute \( x = - 11 \) into \( -2|8 - x| - 6 \):
\( -2|8-(-11)| - 6=-2|19| - 6=-38 - 6=-44
eq - 12 \). So \( x = - 11 \) does not satisfy the equation.

Johan made a sign error when solving for \( x \) (probably when dealing with the absolute - value equation or the signs during the solution process).

Answer:

He is not correct because he made a sign error.