find `x` such that `(-3)/(8)` and `(x)/(-24)`are equivalent rational numbers.

Options

A. -12
B. -9
C. 12
D. 9

Answer

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

### Step 1: Set the two fractions equal to each other.
We start by setting the two fractions equal to each other because equivalent rational numbers have the same value.

\[ \frac{-3}{8} = \frac{x}{-24} \]

### Step 2: Cross-multiply to eliminate the fractions.
To solve for \( x \), we can cross-multiply. This means we multiply the numerator of one fraction by the denominator of the other fraction.

\[ -3 \times (-24) = 8 \times x \]

### Step 3: Simplify the left side.
Now, we calculate the left side:

\[ -3 \times -24 = 72 \]

So, we have:

\[ 72 = 8x \]

### Step 4: Solve for \( x \).
To find \( x \), we divide both sides of the equation by 8:

\[ x = \frac{72}{8} \]

### Step 5: Simplify the fraction.
Now, we simplify \( \frac{72}{8} \):

\[ x = 9 \]

Thus, the value of \( x \) is \( 9 \).

### Final Answer:
\[ x = 9 \]

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