Thread: 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

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

Knowing that , we cross multiply:

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

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.