Answer
Range: $5^{\circ}C $ to $10^{\circ}C $ inclusive, or $[5^{\circ}C,10^{\circ}C]$
Work Step by Step
Given:
$ 41\leq F\leq 50\qquad $
Replace $ F $ with the expression for $ C $
$ 41\displaystyle \leq\frac{5}{9}C+32\leq 50\qquad $
Solve for $ C $. Begin by adding $(-32)$ to all parts:
$ 9\displaystyle \leq\frac{5}{9}C\leq 18\qquad $
Multiply all parts with $\displaystyle \frac{5}{9}$
$9(\displaystyle \frac{5}{9})\leq\frac{5}{9}(\frac{5}{9})C\leq 18(\frac{5}{9})$
$5\leq C\leq 10$
Range: $5^{\circ}C $ to $10^{\circ}C $ inclusive, or $[5^{\circ}C,10^{\circ}C]$
