Answer :
To solve the problem of finding the corresponding Celsius temperature for Fahrenheit temperatures at or below [tex]\(122^\circ F\)[/tex], we start with the equation that relates Celsius ([tex]\(C\)[/tex]) and Fahrenheit ([tex]\(F\)[/tex]):
[tex]\[ F = \frac{9}{5}C + 32 \][/tex]
1. Substitute [tex]\(F\)[/tex] with 122 since that's the maximum we want for the Fahrenheit temperature:
[tex]\[ 122 = \frac{9}{5}C + 32 \][/tex]
2. We want to find the inequality for Celsius. So, replace the equation with an inequality to fit this scenario:
[tex]\[ F \leq 122 \][/tex]
Which implies:
[tex]\[ \frac{9}{5}C + 32 \leq 122 \][/tex]
3. To solve for [tex]\(C\)[/tex], first subtract 32 from both sides of the inequality:
[tex]\[ \frac{9}{5}C \leq 122 - 32 \][/tex]
[tex]\[ \frac{9}{5}C \leq 90 \][/tex]
4. To isolate [tex]\(C\)[/tex], multiply both sides of the inequality by the reciprocal of [tex]\(\frac{9}{5}\)[/tex], which is [tex]\(\frac{5}{9}\)[/tex]:
[tex]\[ C \leq \frac{5}{9} \times 90 \][/tex]
5. Calculate the result:
[tex]\[ C \leq 50 \][/tex]
Thus, the corresponding Celsius temperature that is at or below [tex]\(122^\circ F\)[/tex] is [tex]\(50^\circ C\)[/tex] or less.
[tex]\[ F = \frac{9}{5}C + 32 \][/tex]
1. Substitute [tex]\(F\)[/tex] with 122 since that's the maximum we want for the Fahrenheit temperature:
[tex]\[ 122 = \frac{9}{5}C + 32 \][/tex]
2. We want to find the inequality for Celsius. So, replace the equation with an inequality to fit this scenario:
[tex]\[ F \leq 122 \][/tex]
Which implies:
[tex]\[ \frac{9}{5}C + 32 \leq 122 \][/tex]
3. To solve for [tex]\(C\)[/tex], first subtract 32 from both sides of the inequality:
[tex]\[ \frac{9}{5}C \leq 122 - 32 \][/tex]
[tex]\[ \frac{9}{5}C \leq 90 \][/tex]
4. To isolate [tex]\(C\)[/tex], multiply both sides of the inequality by the reciprocal of [tex]\(\frac{9}{5}\)[/tex], which is [tex]\(\frac{5}{9}\)[/tex]:
[tex]\[ C \leq \frac{5}{9} \times 90 \][/tex]
5. Calculate the result:
[tex]\[ C \leq 50 \][/tex]
Thus, the corresponding Celsius temperature that is at or below [tex]\(122^\circ F\)[/tex] is [tex]\(50^\circ C\)[/tex] or less.
