Answer
For the revenues to exceed the costs, the sales must be higher than 250.
The solution set is (x|x $\gt$ 250), or (250, $\infty$) in interval notation.
Work Step by Step
Let x represent the amount of sales.
The business receives revenue of 48 per sale.
In total, it receives 48 $\times$ x = 48x.
The costs are 4000 + 32 per sale.
In total, the costs are 4000 + 32 $\times$ x = 4000 + 32x
Because revenue needs to exceed the costs, we solve the following inequality.
48x $\gt$ 4000 + 32x
16x $\gt$ 4000
Divide both sides by 16.
x $\gt$ 250
For the revenues to exceed the costs, the sales must be higher than 250.
The solution set is (x|x $\gt$ 250), or (250, $\infty$) in interval notation.
