Answer
Her score on the fourth exam must be 88 or higher.
The solution set is {x|x $\geq$ 88}
Work Step by Step
Her average for her first three exams is 84.
Average for the first three exams = 84 = $\frac{Sum\ of\ three\ exams}{3}$
Multiply both sides by three.
252 = Sum of the first three exams
Let x represent the score for her fourth exam.
Average = $\frac{Sum\ of\ three\ exams\ +\ x}{4}$
Average = $\frac{252\ +\ x}{4}$
Because her average for the four exams should be 85 or higher, we solve the following inequality:
Average $\geq$ 85
$\frac{252\ +\ x}{4}$ $\geq$ 85
Multiply both sides by 4.
252 + x $\geq$ 340
x $\geq$ 88
Her score for the fourth exam must be 88 or higher.
The solution set is {x|x $\geq$ 88}
