Answer
She must get a score of 96 or higher on the fifth exam.
The solution set is {x|x $\geq$ 96}
Work Step by Step
Let x represent the score on the fifth exam.
Her average = $\frac{ 86+88+89+91+x }{5}$
Because her average needs to be 90 or higher, we solve the following inequality.
Average $\geq$ 90
$\frac{ 86+88+89+91+x }{5}$ $\geq$ 90
Multiply both sides by 5.
86+88+89+91+x $\geq$ 450
354 + x $\geq$ 450
x $\geq$ 96
She must get a score of 96 or higher on the fifth exam.
The solution set is {x|x $\geq$ 96}
