Question

Solve the equation by finding the extraneous solutions:
|x-2| = 3x-4

Answer 1

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