Question

Solve the absolute value equation. Check for extraneous solutions. |2x-3|=2x-1

Please show work.

Thank you in advance.

Answer 1

2x - 3 = 2x - 1

- this makes no sense so there is no solution to this equation.

2x - 3 = -(2x - 1)

2x - 3 = -2x + 1

4x = 4

x = 1

Checking this solution:-

2(1) - 3 = -1

-(2(1) - 1) = -1( 1) = -1

So this solution is valid.