|-2/3(x-6)| = 12
|-2/3(x-6)| = 12 expand the inside
|(-2/3)x + 4| = 12
so (-2/3)x + 4 = 12 or (2/3)x - 4 = 12
(-2/3)x = 8 OR (2/3)x = 16
x = -12 OR x = 24
(1,9)
To solve the equation |-2/3(x-6)| = 12, we need to isolate the absolute value expression and then split it into two separate equations. Absolute value equations can be solved by considering both the positive and negative cases.
1. Remove the absolute value bars:
|-2/3(x-6)| = 12
2. Write the equation without the absolute value bars by setting each side equal to the positive and negative versions of the other side:
-2/3(x-6) = 12 or -2/3(x-6) = -12
3. Solve for x in each equation:
-2/3(x-6) = 12 → multiply both sides by -3/2 to eliminate the fraction
(x-6) = -18 → distribute -3/2
x - 6 = -18 → add 6 to both sides
x = -18 + 6 → simplify
x = -12
-2/3(x-6) = -12 → multiply both sides by -3/2 to eliminate the fraction
(x-6) = 18 → distribute -3/2
x - 6 = 18 → add 6 to both sides
x = 18 + 6 → simplify
x = 24
The solutions to the equation |-2/3(x-6)| = 12 are x = -12 and x = 24.