Question

Solve the absolute value equation.

|4x – 1| = 1

(1 point)

Answer 1

The absolute value equation |4x – 1| = 1 can be solved by setting up two separate equations.

First, consider the case where the expression inside the absolute value is positive:
4x - 1 = 1
Add 1 to both sides:
4x = 2
Divide both sides by 4:
x = 1/2

Now consider the case where the expression inside the absolute value is negative:
-(4x - 1) = 1
Multiply through by -1 to change the sign:
4x - 1 = -1
Add 1 to both sides:
4x = 0
Divide both sides by 4:
x = 0

Therefore, the solution to the absolute value equation |4x – 1| = 1 is x = 1/2 or x = 0.