You can
put this solution on YOUR website!4-3|x-2|=-8
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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.
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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:
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-3|x-2| = -12
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Since -3 is the multiplier of the left side, get rid of it by dividing both sides by -3 to
get:
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|x-2| = +4
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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.
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Write this in the form of two equations to be solved. The first equation is:
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+(x-2) = +4
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and the second equation is:
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-(x-2) = +4
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From the first you get:
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x - 2 = +4
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and by adding +2 to both sides you arrive at:
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x = +6 This is one answer that will work.
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And from the second equation you get:
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-(x-2) = +4
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And by removing the parentheses you get:
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-x + 2 = +4
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Subtracting +2 from both sides reduces this equation to:
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-x = +2
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And finally, we are trying to solve for x not for -x. So we multiply both sides by -1 to
arrive at:
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x = -2 This is a second solution to this problem.
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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.
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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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