Setup and solve the absolute value equation. Don't forget to check for extraneous solutions.
The absolute value of (three x plus five) equals twelve x plus 8.
|3x + 5| = 12x + 8
3x + 5 = 12x + 8
3x - 12x = 8 - 5
-9x = 3
x = -3
Check for extraneous solutions:
|3(-3) + 5| = 12(-3) + 8
|-9 + 5| = -36 + 8
|-4| = -36 + 8
4 = 44
This is not true, so the only solution is x = -3.
NOPE, the robot tutor screws up again.
|3x + 5| = 12x + 8 , preliminary restriction: 3x+5 ≥ 0 -----> x ≥ -5/3
3x+5 = 12x + 8 OR -3x - 5 = 12x + 8
9x = -3 OR -15x = 13
x = -1/3 OR x = -13/15 <---- reject since -13/5 < -5/3
so x = -1/3
btw, the robot did not even consider the 2nd case, which could have
yielded a second number.
Secondly , notice how the robot went from -9x = 3 to
x = -3 !!!!