SOLUTION: Solve for x in the inequality: -1 is less than (x+2)/(x-3) Any tips, tricks, advice for other inequality problems is greatly appreciated as well as help with this problem! Th

, with  as this would make the denominator 0, and therefore, an UNDEFINED inequality 

 ----- Multiplying both sides by LCD, x - 3



 -------- Subtracting 3 from both sides



 --------- Subtracting x from both sides



 -------- Inequality sign changes when dividing by a negative value



Now, we have the CRITICAL VALUES:  

This means that we will have THREE (3) TEST-INTERVALS to determine whether or not values

in the intervals SATISFY the ORIGINAL inequality: . These TEST INTERVALS are:

1)   

2)   , and

3)   



Testing  with test value: ,  becomes: 





As the above is TRUE, the test-interval:  IS a solution



Testing  with test value: ,  becomes: 





As the above is FALSE, the test-interval:  IS NOT a solution



Testing  with test value: ,  becomes: 





As the above is TRUE, the test-interval:  IS a solution

In interval notation, this is: (- oo, ½) ᑌ (3, oo) , or () ᑌ ()