Absolute Value Equations: Solving |2x-8| + |12-3x| = 0

[Nelo]

Homework Statement

|2x-8| + |12 - 3x | = 0

Homework Equations

what do i do when it = 0

The Attempt at a Solution

I tried solving it like all the others, but i know there is a unique thing to do when it = 0, i jus don't know what.

So , here's what i did.

2|x-4| + -3|x-4| = 0
-|x-4| = 0

x > 4

(-)x-4 = 0
-x = 4
x = -4

x < 4

(-)-x+4 = 0
x+4 = 0
x = - 4.

The answer is 4, I just probably set the normal one up wrong, what am i doing wrong?

 

[Mark44]

Homework Statement

|2x-8| + |12 - 3x | = 0

Homework Equations

what do i do when it = 0

The Attempt at a Solution

I tried solving it like all the others, but i know there is a unique thing to do when it = 0, i jus don't know what.

So , here's what i did.

2|x-4| + -3|x-4| = 0
-|x-4| = 0

x > 4

(-)x-4 = 0
-x = 4
x = -4

x < 4

(-)-x+4 = 0
x+4 = 0
x = - 4.

The answer is 4, I just probably set the normal one up wrong, what am i doing wrong?

|12 - 3x | = |3x - 12| = 3|x - 4|