Question

Solve the following inequality and write your answer using interval notation. Please show all of your work. 50/x+4 +1<4x

Answer 1

You need to get an equivalent inequality with 0 on one side
\[\frac{50}{x+4}+1<4x\]
\[\frac{50}{x+4}+1-4x<0\]
\[\frac{50+(x+4)-4x(x+4)}{x+4}<0\]
\[\frac{-4x^2-15x+54}{x+4}<0\]

Answer 2

Now you have a critical value of x=-4
You must also solve the zeros of the numerator.
This will divide the x-axis into intervals.
All values in each interval will be either positive or negative
You're looking for the intervals which result in a negative