SOLUTION: Looking for absolute value on both sides: 5/2 - x = 2 - x/2 The answer is 1,3 but I can't figure out how to do the problem to arrive at the answer. Any help is greatly

Algebra ->  Algebra  -> Absolute-value -> SOLUTION: Looking for absolute value on both sides: 5/2 - x = 2 - x/2 The answer is 1,3 but I can't figure out how to do the problem to arrive at the answer. Any help is greatly       Log On

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Question 62346: Looking for absolute value on both sides:
5/2 - x = 2 - x/2
The answer is 1,3 but I can't figure out how to do the problem to arrive at the answer. Any help is greatly appreciated!
Answer by joyofmath(189) About Me  (Show Source):
You can put this solution on YOUR website!
abs%285%2F2+-+x%29+=+abs%282+-+x%2F2%29.
The idea here is that if abs%28a%29+=+abs%28b%29 then either a=b or a=-b. For example, abs%287%29+=+abs%28-7%29 because 7+=+-%28-7%29.
So, there are two equations to solve: 5%2F2-x+=+2-%28x%2F2%29 and 5%2F2-x+=+-%282-%28x%2F2%29%29.
Let's solve the first one: 5%2F2-x+=+2-%28x%2F2%29.
Add x/2 to both sides: 5%2F2-x%2F2+=+2.
Subtract 2 from both sides: 1%2F2-x%2F2=0.
Multiply both sides by 2: 1-x+=+0 so x=1. That's the first answer.
Let's solve the second equation: 5%2F2-x+=+-%282-%28x%2F2%29%29.
First, let's simplify the right side of the equation: 5%2F2-x+=+-2%2Bx%2F2.
Add 2 to both sides of the equation: 9%2F2-x+=+x%2F2.
Add x to both sides of the equation: 9%2F2+=+3x%2F2.
Multiply both sides of the equation by 2: 9=3x sp x=3 which is the 2nd answer.