SOLUTION: 4-3|x-2|=-8 Thank you for your help. Tammi

Question 71703This question is from textbook Intermediate Algebra
: 4-3|x-2|=-8
Thank you for your help.
Tammi This question is from textbook Intermediate Algebra

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
4-3|x-2|=-8
.
Up to a point, you can work this just as you would work a normal equation. With that in
mind, your initial task is to get all the numbers on the right side of the equal sign and
the term involving x on the left side.
.
So lets start by subtracting 4 from both sides to get rid of the 4 on the left side.
After you do that subtraction you have changed the equation to:
.
-3|x-2| = -12
.
Since -3 is the multiplier of the left side, get rid of it by dividing both sides by -3 to
get:
.
|x-2| = +4
.
Here's a way that I now would look at this problem. Look at the quantity inside the absolute
value signs. It can either be +(x-2) or it can be -(x-2) and the absolute value signs
will change it to +(x-2) so both of these [+(x-2)] and [-(x-2)] will work.
.
Write this in the form of two equations to be solved. The first equation is:
.
+(x-2) = +4
.
and the second equation is:
.
-(x-2) = +4
.
From the first you get:
.
x - 2 = +4
.
and by adding +2 to both sides you arrive at:
.
x = +6 This is one answer that will work.
.
And from the second equation you get:
.
-(x-2) = +4
.
And by removing the parentheses you get:
.
-x + 2 = +4
.
Subtracting +2 from both sides reduces this equation to:
.
-x = +2
.
And finally, we are trying to solve for x not for -x. So we multiply both sides by -1 to
arrive at:
.
x = -2 This is a second solution to this problem.
.
The two answers to this problem are x = +6 and x = -2. Check them by substituting
them into the original problem and you will find that they work.
.
I hope this helps you by providing a way you can work absolute value problems. Not everyone
works these problems this way, but I find it easy for me to understand and remember.
Maybe you will too.
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