Solve the equation. | 6 x $-$ 42 | + 6 = 24
A) x = 4
B) x = $-$ 4, x = $-$ 10
C) x = 10
D) x = 4, x = 10

Question

Quizplus · Accepted Answer

First, we simplify the absolute value expression: |6x - 42| = 6
Then we solve for x in both cases:
6x - 42 = 6
6x = 48
x = 8
or
-(6x - 42) = 6
-6x + 42 = 6
-6x = -36
x = 6
So the possible solutions are x = 6 or x = 8. But we need to check if any of them makes the left side of the original equation negative, which is not allowed since absolute values are always non-negative. 
For x = 6: |6(6) - 42| + 6 = 24, which works.
For x = 8: |6(8) - 42| + 6 = 30, which doesn't work.
Thus, the only solution is x = 6. However, in the answer choices, there is also x = 10 that was not found through the above method. We can check if it works:
|6(10) - 42| + 6 = 24, which also works. Therefore, the answer is D: x = 6, x = 10.

Solve the Equation −-− 42 | + 6 = 24 A) X = 4

Solve the Equation $-$ 42 | + 6 = 24
A) X = 4