# How do you solve this inequality?

• Nov 24th 2012, 12:27 AM
aroe
How do you solve this inequality?
|1-x|<|2x-5|
• Nov 24th 2012, 12:35 AM
Prove It
Re: How do you solve this inequality?
• Nov 24th 2012, 12:38 AM
aroe
Re: How do you solve this inequality?
Quote:

Originally Posted by Prove It

I did. It got me more confused. Can you explain this one too? Maybe I'll get it. I'm not used to the way you handled it. BTW the answer I get is x<2 or x>4.
• Nov 24th 2012, 01:03 AM
Deveno
Re: How do you solve this inequality?
using MarkFL2's clever approach, note that |a| = √(a2).

so |1-x| < |2x-5| is the same as:

√(1-x)2 < √(2x-5)2

squaring both sides:

(1-x)2 < (2x-5)2

1-2x+x2 < 4x2-20x+25

0 < 3x2-18x+24

0 < x2-6x+8

0 < (x-2)(x-4) <---for this to be true, both factors must be either both positive, or both negative.
• Nov 24th 2012, 01:07 AM
aroe
Re: How do you solve this inequality?
Quote:

Originally Posted by Deveno
using MarkFL2's clever approach, note that |a| = √(a2).

so |1-x| < |2x-5| is the same as:

√(1-x)2 < √(2x-5)2

squaring both sides:

(1-x)2 < (2x-5)2

1-2x+x2 < 4x2-20x+25

0 < 3x2-18x+24

0 < x2-6x+8

0 < (x-2)(x-4) <---for this to be true, both factors must be either both positive, or both negative.

That would mean the answer is x>4 or x<2 which is the same answer I get.
• Nov 24th 2012, 01:10 AM
aroe
Re: How do you solve this inequality?
I still like the other method Proveit used. If he can solve it again that way that would be great.
• Nov 24th 2012, 01:16 AM
Prove It
Re: How do you solve this inequality?
I'm not going to do your work for you. You know the procedure, you can try it!
• Nov 24th 2012, 01:19 AM
aroe
Re: How do you solve this inequality?
Sorry I miswrote the question it's actually
|1-x|>|2x-5|

And I can't find an answer for it.
• Nov 24th 2012, 01:56 AM
MarkFL
Re: How do you solve this inequality?
Since you found:

$|1-x|<|2x-5|$

gives the solution $(-\infty,2)\,\cup\,(4,\infty)$

then you may state:

$|1-x|>|2x-5|$

gives the solution $(2,4)$