Answer
Range of Fahrenheit Temperature\[{{59}^{\circ }}\le F\le {{95}^{\circ }}\]
Work Step by Step
The desired temperature range in Fahrenheit can be computed by solving the following double-sided inequality.
\[\begin{align}
& {{15}^{\circ }}\le \frac{5}{9}\left( F-32 \right)\le {{35}^{\circ }} \\
& {{\left( 15\times 9 \right)}^{\circ }}\le \frac{5}{9}\left( F-32 \right)\times 9\le {{\left( 35\times 9 \right)}^{\circ }} \\
& {{135}^{\circ }}\le 5\left( F-32 \right)\le {{315}^{\circ }} \\
& {{\left( \frac{135}{5} \right)}^{\circ }}\le \left( F-32 \right)\le {{\left( \frac{315}{5} \right)}^{\circ }}
\end{align}\]
This can be further simplified as follows:
\[\begin{align}
& {{27}^{\circ }}\le \left( F-32 \right)\le {{63}^{\circ }} \\
& {{\left( 27+32 \right)}^{\circ }}\le \left( F-32+32 \right)\le {{\left( 63+32 \right)}^{\circ }} \\
& {{59}^{\circ }}\le F\le {{95}^{\circ }}
\end{align}\]
