Find the integer x such that `(3)/(8) and (x)/((- 24))` are equivalent fractions.

Options

A. `-19`
B. `-9`
C. 6
D. 9

Answer

To find the integer \( x \) such that \( \frac{3}{8} \) and \( \frac{x}{-24} \) are equivalent fractions, we can follow these steps:

### Step 1: Set up the equation for equivalent fractions
Since \( \frac{3}{8} \) and \( \frac{x}{-24} \) are equivalent, we can set up the equation:
\[ \frac{3}{8} = \frac{x}{-24} \]

### Step 2: Cross-multiply
To eliminate the fractions, we will cross-multiply:
\[ 3 \times (-24) = 8 \times x \]
This simplifies to:
\[ -72 = 8x \]

### Step 3: Solve for \( x \)
Now, we need to isolate \( x \). We can do this by dividing both sides of the equation by 8:
\[ x = \frac{-72}{8} \]
Calculating the right side gives:
\[ x = -9 \]

### Conclusion
The integer \( x \) such that \( \frac{3}{8} \) and \( \frac{x}{-24} \) are equivalent fractions is:
\[ \boxed{-9} \]

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