The equation Upper F equals nine fifths Upper C plus 32

Question

gives the relationship between temperatures measured in degrees Celsius and degrees Fahrenheit. Use an inequality to represent the corresponding Celsius temperature that is at or below 86 degrees Upper F.

Answer 1

To find the corresponding Celsius temperature that is at or below 86 degrees Fahrenheit using the given equation \( F = \frac{9}{5}C + 32 \), we start by substituting \( F \) with 86.

1. Substitute \( F \) with 86 in the equation: \[ 86 = \frac{9}{5}C + 32 \]

2. Next, we can solve for \( C \) by first isolating the term with \( C \): \[ 86 - 32 = \frac{9}{5}C \] \[ 54 = \frac{9}{5}C \]

3. Multiply both sides by \( \frac{5}{9} \) to solve for \( C \): \[ C = 54 \cdot \frac{5}{9} \] \[ C = 30 \]

So, \( C = 30 \) degrees Celsius corresponds to 86 degrees Fahrenheit.

Now, to represent the condition that the Celsius temperature is at or below 86 degrees Fahrenheit, we can write the inequality: \[ F \leq 86 \]

Converting this to an equivalent inequality in terms of Celsius gives us: \[ \frac{9}{5}C + 32 \leq 86 \]

This is the inequality representing the condition. To isolate \( C \):

1. Subtract 32 from both sides: \[ \frac{9}{5}C \leq 54 \]

2. Multiply both sides by \( \frac{5}{9} \): \[ C \leq 30 \]

Thus, the final inequality representing the corresponding Celsius temperature that is at or below 86 degrees Fahrenheit is: \[ C \leq 30 \]