Answer
She must receive a score of 89 or higher on the exam.
The solution set is {x|x $\geq$ 89}.
Work Step by Step
Let x represent the score on the fifth exam.
Her average is $\frac{83+89+78+86+x}{5}$.
Because her average should be 85 or higher, we solve the following inequality.
Average $\geq$ 85
$\frac{83+89+78+86+x}{5}$ $\geq$ 85
Multiply both sides by 5.
83+89+78+86+x $\geq$ 425
336 + x $\geq$ 425
x $\geq$ 89
She must receive a score of 89 or higher on the exam.
The solution set is {x|x $\geq$ 89}.
