SOLUTION: 5+X<2X+1<6-X Can anyone help me understand how to solve this?

Algebra ->  Algebra  -> Inequalities -> SOLUTION: 5+X<2X+1<6-X Can anyone help me understand how to solve this?      Log On

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Question 124822: 5+X<2X+1<6-X
Can anyone help me understand how to solve this?
Answer by solver91311(12126) About Me  (Show Source):
You can put this solution on YOUR website!
5%2BX%3C2X%2B1%3C6-X

There are actually two relationships established here. Deal with each one separately.
5%2Bx%3C2x%2B1

Add -1 to each side.
4%2Bx%3C2x

Add -x to each side.
4%3Cx

Now look at the other relationship
2x%2B1%3C6-x

Add -1 to each side
2x%3C5-x

Add x to each side
3x%3C5

Divide by 3. (since we are dividing by a positive number, we keep the sense of the inequality as it is)
x%3C5%2F3

So, x must simultaneously be less than 5/3 and greater than 4. Impossible. There is no value of x that makes the original inequality a true statement.