Answer
$\$1750 \leq x \leq \$3750$
Work Step by Step
Current savings: $\$500$
Number of summers spent working: $2$
Total goal savings: $\$4000 \leq 2x+500 \leq \$8000$
Subtract $\$500$
$\$4000-\$500 \leq 2x\leq \$8000-\$500$
$\$3500 \leq 2x \leq \$7500$
Divide by $2$.
$\frac{$3500}{2} \leq x \leq \frac{$7500}{2}$
Range of money Carol must save each summer: $\$1750 \leq x \leq \$3750$