Question

How do you solve `5x – 4 = |2x + 1|` and find any extraneous solutions?

Answer 1

`x=5/3`

Explanation:

The solutions for `5x – 4 = |2x + 1|`

are contained in the set of solutions for `(5x-4)^2-(2x+1)^2 =0`

but

`(5x-4)^2-(2x+1)^2=(3 x-5) (7 x-3)=0` so

`x={3/7, 5/3}` and the feasible solution is `x=5/3` because it verifies the original relationship.