Elementary Algebra

Her score on the fourth exam must be 88 or higher. The solution set is {x|x $\geq$ 88}
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}