One Quick Algebra II Question? I don't get it

Hello!
I have a math question I don't really understand. I don't think I'm doing it right. (Worst subject ever!)

Solve the equation and write the solution set.
|4x – 8| – 3x = 6x + 2

So, here's what I've done.
4x - 8 would be -4x then its absolute value would be 4x.

So, it would be;
4x – 3x = 6x + 2

Then 6x + 2 = 8x
4x – 3x = 8x

4x – 3x = 1x

So, the final part would be 1x = 8x.
Is that right? I don’t think so.
What would be the solution set? Anything between 1 and 8?

Any help would be appreciated! Thanks!

No: you can't make the statement:
"4x - 8 would be -4x then its absolute value would be 4x." because this is NOT true. As you can seee, this leads you to 1x = 8x, which would be true only if x = 0


So, look at what you are starting with:
|4x - 8| - 3x = 6x + 2
You can add 3x to both sides, so
|4x - 8| = 9x + 2

Now, look at |4x - 8| you can take out the common factor (4)
= 4 |x - 2|
so 4|x - 2| = 9x + 2
==> |x - 2| = 9x/4 + 1/2

You can now look at |x - 2| as being either positive or negative

So: either (x - 2) = 9x/4 + 1/2
or -(x - 2) = 2 - x = 9x/4 + 1/2

if x - 2 = 9x/4 + 1/2
then 9x/4 - x = -2 - 1/2 = -5/2
==> 5x/4 = -5/2
==> x = -2

if 2-x = 9x/4 + 1/2
then 2 - 1/2 = 3/2 = 13x/4
==> 13x = 6
==> x = 6/13

So your solution set is (-2, 6/13)

(expand brackets) ... 4x-8-3x = 6x + 2 (simplify the left side) ... x - 8 = 6x + 2 (minus x so that you only have it on one side) ... -8 = 5x + 2 (minus 2 so that you only have individual numbers on one side) ... -10 = 5x (divide -10 by 5 to get your final answer) ... x = -2
To check you just insert the number -2 wherever x is mentioned and see if the equation works - which it does!
REMEMBER: Whatever you do to one side of the equation, you must do to the other
Source(s):
ME! xD

|4x – 8| – 3x = 6x + 2
==> |4x-8| = 9x + 2

a) Assume 4x-8>=0, then 4x-8 = 9x+2 ==> x = -2. However, when x=-2, 4x-8=-16<0. So it is not a solution.

b) Assume 4x-8<0, then -4x+8 = 9x+2 ==> x = 6/13. 4x-8 = 4*(6/13) - 8 < 0. So it is a solution.

In summary, x = 6/13.

9x + 2 = |8 - 4x|
SOOOOOOOOOOOOOOOOOOOOOOOOO the answer's 6/13





..... i think.