Thread: How do you solve this inequality?

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

Follow the same procedure I outlined in your last question.

Originally Posted by Prove It

Follow the same procedure I outlined in your last question.

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.

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.

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.

I still like the other method Proveit used. If he can solve it again that way that would be great.

I'm not going to do your work for you. You know the procedure, you can try it!

Sorry I miswrote the question it's actually
|1-x|>|2x-5|

And I can't find an answer for it.

Since you found:



gives the solution

then you may state:



gives the solution