Solve the equation by finding the extraneous solutions:

|x-2| = 3x-4

If you have

|a|=b

assume

a=b and - a=b

|x-2|=3x-4

assume

x-2=-3x-4

- (x-2) = 3x-4

solve each

x-2=3x-4

minus x from both sides

-2=2x-4

add 4 to both sides

2=2x

divide both sides by 2

1=x

- (x-2) = 3x-4

-x+2=3x-4

add x to both sides

2=4x-4

add 4 to both sides

6=4x

divide both sides by 4

1.5=x

x=1 or 1.5