Temperature measured in degrees Fahrenheit (F) are related to temperature measured in degree Celcius (C) by the formula `F = 9/5 C +32`. There is 1 value of x for which x degree Fahrenheit equls x degrees Celsius. What is that value?

Options

A. `-72`
B. `-40`
C. `-32`
D. `0`

Answer

To find the value of \( x \) for which \( x \) degrees Fahrenheit equals \( x \) degrees Celsius, we start with the given formula:

\[ F = \frac{9}{5}C + 32 \]

Since we want to find the temperature where \( x \) degrees Fahrenheit equals \( x \) degrees Celsius, we can set \( F \) and \( C \) to \( x \):

\[ x = \frac{9}{5}x + 32 \]

Now, we will solve for \( x \).

### Step 1: Rearranging the equation
First, we rearrange the equation to isolate \( x \):

\[ x - \frac{9}{5}x = 32 \]

### Step 2: Combining like terms
To combine the terms on the left side, we need a common denominator. The common denominator for \( x \) (which is \( \frac{5}{5}x \)) and \( \frac{9}{5}x \) is \( 5 \):

\[ \frac{5}{5}x - \frac{9}{5}x = 32 \]

This simplifies to:

\[ \frac{5x - 9x}{5} = 32 \]

### Step 3: Simplifying the left side
Now, we simplify the left side:

\[ \frac{-4x}{5} = 32 \]

### Step 4: Eliminating the fraction
To eliminate the fraction, we multiply both sides by \( -5 \):

\[ -4x = 32 \times -5 \]

Calculating the right side gives:

\[ -4x = -160 \]

### Step 5: Solving for \( x \)
Now, we divide both sides by \( -4 \):

\[ x = \frac{-160}{-4} = 40 \]

### Final Answer
Thus, the value of \( x \) for which \( x \) degrees Fahrenheit equals \( x \) degrees Celsius is:

\[ \boxed{-40} \]