How do you solve and write the following in interval notation: 10x/(2x + 7)> 5?

1 Answer
Jan 2, 2018

x< -\frac{7}{2}

Explanation:

10\frac{x}{2x+7}>5

\frac{10x}{2x+7}>5

\frac{10x}{2x+7} -5 >0

\frac{10x -5(2x+7)}{2x+7} >0

\frac{10x -10x-35}{2x+7} >0

\frac{-35}{2x+7} >0

-\frac{35}{2x+7} >0

\frac{35}{2x+7} <0

Now let's check where the denominator is < 0
2x+7 < 0

2x<-7

The solution:
x< -\frac{7}{2}