A student was trying to solve the equation below but made an error. Find and explain the error
-2(x + 2) = 6x + 12
-2x + 4 = 6x + 12
-6x -6x
-8x + 4 = 12
-4 -4
-8x divided by -8 = 8 divided by -8
x = -1
The error in the student's solution is in the step where they subtracted 6x from both sides of the equation. Instead of subtracting 6x from both sides, they mistakenly added 6x to both sides. This mistake resulted in a sign error in the x terms. If the correct subtraction was done, the equation would have been:
-2(x + 2) = 6x + 12
-2x - 4 = 6x + 12
-2x - 6x = 12 + 4
-8x = 16
So, the correct solution would be:
x = 16 / -8 = -2
Thus, the correct value for x is -2, not -1 as the student mistakenly found.