Solve the compound inequality. Other than ∅, use interval notation to express the solution set and graph the
solution set on a number line.
-The formula for converting Celsius temperature, C, to Fahrenheit temperature, F, is
$$\mathrm { F } = \frac { 9 } { 5 } \mathrm { C } + 32$$
If Fahrenheit temperature ranges from $- 58 ^ { \circ }$ to $41 ^ { \circ }$, inclusive, what is the range for the Celsius temperature?
A) $\left[ - 50 ^ { \circ } \mathrm { C } , 5 ^ { \circ } \mathrm { C } \right]$
B) $\left( - 50 ^ { \circ } \mathrm { C } , 5 ^ { \circ } \mathrm { C } \right)$
C) $\left[ - 72 ^ { \circ } \mathrm { C } , 106 ^ { \circ } \mathrm { C } \right]$
D) $\left( - 72 ^ { \circ } \mathrm { C } , 106 ^ { \circ } \mathrm { C } \right)$

Question

Quizplus · Accepted Answer

To find the Celsius range corresponding to the Fahrenheit range of $-58^\circ$ to $41^\circ$, we use the conversion formula $F = \frac{9}{5}C + 32$. For $F = -58^\circ$, we solve for $C$ as follows:$$-58 = \frac{9}{5}C + 32$$Subtracting 32 from both sides gives:$$-90 = \frac{9}{5}C$$Multiplying both sides by $\frac{5}{9}$ gives:$$C = -50^\circ$$For $F = 41^\circ$, we solve for $C$ similarly:$$41 = \frac{9}{5}C + 32$$Subtracting 32 from both sides gives:$$9 = \frac{9}{5}C$$Multiplying both sides by $\frac{5}{9}$ gives:$$C = 5^\circ$$Therefore, the Celsius temperature range is $[-50^\circ C, 5^\circ C]$.

Solve the Compound Inequality F=95C+32\mathrm { F } = \frac { 9 } { 5 } \mathrm { C } + 32F=59​C+32

Solve the Compound Inequality $\mathrm { F } = \frac { 9 } { 5 } \mathrm { C } + 32$