# Thread: How do you solve this inequality?

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

3. ## Re: How do you solve this inequality?

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.

4. ## 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.

5. ## Re: How do you solve this inequality?

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.

6. ## 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.

7. ## 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!

8. ## 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.

9. ## Re: How do you solve this inequality?

Since you found:

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

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

then you may state:

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

gives the solution $\displaystyle (2,4)$