# Thread: Solving Inequality for X

1. ## Solving Inequality for X

I'm trying to solve 1/(2-x) > 1/2 for x, where 0 < x < 1. The problem is, I'm getting x < 0 where as I think it should be x > 0. I know you need to flip the inequality when multiplying or dividing by a negative number, but this isn't coming up at all. What am I missing?

1/(2-x) > 1/2 Since 0 < x < 1, (2-x) is never negative and multiplying by it does not switch the inequality

2 > 2 - x

0 > x

2. ## Re: Solving Inequality for X

Originally Posted by Relmiw
I'm trying to solve 1/(2-x) > 1/2 for x, where 0 < x < 1. The problem is, I'm getting x < 0 where as I think it should be x > 0. I know you need to flip the inequality when multiplying or dividing by a negative number, but this isn't coming up at all. What am I missing?

1/(2-x) > 1/2 Since 0 < x < 1, (2-x) is never negative and multiplying by it does not switch the inequality

2 > 2 - x

0 > x
$\displaystyle \frac{1}{2-x}>\frac{1}{2}$

Knowing that $\displaystyle 2-x>0$, we cross multiply:

$\displaystyle 2>2-x$

$\displaystyle -x<0$

$\displaystyle x>0$

3. ## Re: Solving Inequality for X

ahhhh, thanks. I should have known. once I got to -x < 0 i would instinctively drop the -1 even knowing i was on the lookout for it

4. ## Re: Solving Inequality for X

Originally Posted by Relmiw
ahhhh, thanks. I should have known. once I got to -x < 0 i would instinctively drop the -1 even knowing i was on the lookout for it
I did that too when I first tackled the question.