Answer:
x = 15/16
Explanation:
Before we can begin solving, we need to isolate everything inside the absolute value brackets:
(4x = 6 - |4x - 3/2|) - 6
(4x - 6 = - |4x - 3/2|) / -1
-4x + 6 = |4x - 3/2|
Because we have an absolute value equation, we make two separate equations with a positive and negative answer since any positive number and its negative equivalent have the same absolute value (e.g. |5| = 5 and |-5| = 5):
- Note that for any absolute value equation, there's a chance to have 0 solutions, 1 solution, or 2 solutions
Positive answer:
- Also note that for the positive answer, we don't change anything on the left-hand side.
(-4x + 6 = 4x - 3/2) + 4x
(6 = 8x - 3/2) + 3/2
(15/2 = 8x) / 8
(15/2 = 8x) * 1/8
15/16 = x
Thus, one of the answers for x is 15/16.
Negative answer:
- For the negative answer, we must multiply the left-hand side by -1:
-1(-4x + 6) = 4x - 3/2
(4x - 6 = 4x - 3/2) - 4x
-6 = -3/2
Because the equation is not true, there is only one answer for the absolute value equation.