Jon C. answered • 10/11/12

CCSS Master of Making Math and Music Fun from K-12

Solve (x+1)/(2-x)>2

1. (2-x)•(x+1)/(2-x) >2 (2-x) multiply both sides by the denominator...

_{remember you can always get rid of a denominator by multiply EVERYTHING by that denominator :)}

2. (x+1) > 2(2-x) simplify the right side using the Distributive Property

3. (x+1) > 4 - 2x To solve this inequality, x's on one side, and constants (terms with numbers and no variables). To do this, add 2x to both sides and subtract one from both sides, leaving you with: 3x > 3

4. 3x > 3, so x>1. Now we must consider any type of inconsistency of siginifiacnt x values, for instance the one that makes the original denominator zero.

What value of x makes (x+1)/(2-x) undefined (zero on bottom). Well this is easy.... 2-x = 0, so x=2. This means that the expression is undefined at x=2, so even though we got x>1 before, we now know x ≠ 2. Can it equal any number larger than two? Try 3 and 4 and see if you can find a pattern.

(x+1)/(2-x)>2 for x=3 is (3+1)/(2-3)>2

4 / -1 > 2 NO GOOD!

(x+1)/(2-x)>2 for x=4 is (4+1)/(2-4)>2

5 / -2 > 2 NO GOOD!

As you should notice, with any number larger than 2, the left side is negative which will NEVER be >2.

Summary: we found x > 1, that x≠2 or any number larger than two, so our solution is 1 < x < 2.

Thanks for your time. Hope this helps :)

so the answer is 1 < x < 2.