Absolute Value on both sides of Equals Sign... :) How to solve?

Question

Ok, Im stumped :)

When theres a problem like:

| -3x + 4 | = | -x + 2 |

how do you solve this?

Thank you.

Answer 1

There are 3 steps to solve

1) x>=2 then -3x+4=-x+2  => 2x= 2    x=1 (out of the range)

2) 4/3<x<2 then    +3x-4=-x+2    4x=6    x=3/2 (within the range)

3) x<4/3   then    3x-4= x-2        2x=2   x=1    (within the range)

Answers:  x1=3/2     x2=1

          

Answer 2

Divide into intervals

  -3x+4=0 x=4/3 sign +++++4/3--------

                                        -x+2=0  x=2 sign  +++++++2----------

so  x<4/3 both sides are positive and

--3x+4=-x+2  -2x= --2  so x=1 Ok

4/3<x<2   3x-4 = -x+2  4x=6 so x= 3/2  OK

Finally

x>2  

3x-4=x-2 2x=2   x= 1 Not a solution