SOLUTION: I have problems trying to understand rational inequalities. How does the equation 4x<16/(x+3) become 0<-4(x+4)(x-1)/(x+3)? what steps were taken, in other words, to get the equatio

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I have problems trying to understand rational inequalities. How does the equation 4x<16/(x+3) become 0<-4(x+4)(x-1)/(x+3)? what steps were taken, in other words, to get the equatio      Log On


   

Question 675746: I have problems trying to understand rational inequalities. How does the equation 4x<16/(x+3) become 0<-4(x+4)(x-1)/(x+3)? what steps were taken, in other words, to get the equation -4(x+4)(x-1) after moving 4x to the other side to get 0 on one side?
Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
4x+%3C+16%2F%28x%2B3%29
...
Multiply both sides by (x+3)
4x%28x%2B3%29+%3C+%2816%2Fcross%28%28x%2B3%29%29%29%28cross%28x%2B3%29%29
4x(x+3) < 16
4x(x+3) - 16 < 0
...
Distribute the 4x
4x%5E2+%2B+12x+-+16+%3C+0
4%28x%5E2+%2B+3x+-+4%29+%3C+0
4(x-1)(x+4) < 0
OR
4x%5E2%2B12x-16%3C0
0%3C-4x%5E2+-+12x+%2B+16
0%3C-4%28x%5E2%2B3x-4%29
0%3C-4%28x%2B4%29%28x-1%29
...
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