SOLUTION: Can amyone help me figure out this Absolute Value problem: 4-3 | x - 2 | = -8 I'm sure it is simple but it is not so simple for me tonight. Please expalin steps to isolat

Question 7770: Can amyone help me figure out this Absolute Value problem:
4-3 | x - 2 | = -8
I'm sure it is simple but it is not so simple for me tonight.
Please expalin steps to isolate the absolute value.
Found 2 solutions by prince_abubu, Earlsdon:
Answer by prince_abubu(198) (Show Source): You can put this solution on YOUR website!
Alright. The 4 is not being multiplied by the absolute value, so move it to the right by subtracting it. So far, you should get:

<--- combined the -4 and the -8.

<---- divide both sides by -3.

Now here's the tricky part. Just by looking at it, it's so tempting to say that x = 6 because 6 - 4 = 2. And that's right. BUT, there is ANOTHER solution!

Actually, when you solve absolute value equations, you actually solve 2 equations. In this case, the two are which was what we did, and . Why, though, do we do that!?

We know that |4| = 4, right? So we set the inside of the absolute value x - 2 to equal four. BUT we also know that |-4| = 4. AHA! So it then makes sense to set the inside of the absolute value equal to -4. After all, it'll turn that -4 into a positive 4.

SO, let's nail down the x - 2 = -4 also. It turns out (by adding 2 to both sides) that x = -2. If we plugged that into the absolute value, we have |-2 - 2| = |-4| = 4.

So your solutions are 6 and -2.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Treat this as though you were solving a regular equation until you come to removing the absolute-value bars.
4 - 3|x - 2| = -8 Subtract 4 from both sides.
-3|x - 2| = -12 Divide both sides by -3.
|x - 2| = 4 Now remove the bars and write two equations:
x - 2 = 4 and x - 2 = -4 Now, solve each of these for x.
x - 2 = 4, then x = 6 and x - 2 = -4, then x = -2
So, you have two solutions:
x = 6 and
x = -2
Check:
x = 6 first: Remember that | 4 | = 4
4 - 3|6 - 2| = 4 - 3|4| = 4 - 3(4) = 4 - 12 = -8
now x = -2: Remember that |-4| = 4
4 - 3|-2-2| = 4 - 3|-4| = 4 - 3(4) = 4 - 12 = -8
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