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

1 Answer
Jan 2, 2018

Answer:

#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}#