Answer:
So, the solutions for the equation |4x - 1| = 12 are x = 13/4 and x = -11/4
Explanation:
To solve the equation |4x - 1| = 12, we can split it into two cases based on the possible values of the expression inside the absolute value:
Case 1: 4x - 1 ≥ 0
If 4x - 1 ≥ 0, then we can drop the absolute value and solve for x:
4x - 1 = 12
4x = 13
x = 13/4
Therefore, x = 13/4 is a solution for this case.
Case 2: 4x - 1 < 0
If 4x - 1 < 0, then the absolute value will become its opposite, and we will solve for x with a negative answer:
-(4x - 1) = 12
-4x + 1 = 12
-4x = 11
x = -11/4
Therefore, x = -11/4 is a solution for this case.
So, the solutions for the equation |4x - 1| = 12 are x = 13/4 and x = -11/4