If `6(1)/(x)xx(4)/(5)=5` what is x ?

Options

A. 4
B. 10
C. 8
D. 6

Explanation

To solve the equation \( \frac{6}{x} \cdot \frac{4}{5} = 5 \), we will follow these steps:

### Step 1: Write the equation
We start with the given equation:
\[ \frac{6}{x} \cdot \frac{4}{5} = 5 \]

### Step 2: Simplify the left side
We can simplify the left side of the equation:
\[ \frac{6 \cdot 4}{5x} = 5 \]
This simplifies to:
\[ \frac{24}{5x} = 5 \]

### Step 3: Cross-multiply
To eliminate the fraction, we can cross-multiply:
\[ 24 = 5x \cdot 5 \]
This simplifies to:
\[ 24 = 25x \]

### Step 4: Solve for x
Now, we will solve for \( x \) by dividing both sides by 25:
\[ x = \frac{24}{25} \]

### Step 5: Check the answer
We can check our answer by substituting \( x \) back into the original equation:
\[ \frac{6}{\frac{24}{25}} \cdot \frac{4}{5} = 5 \]
Calculating the left side:
\[ \frac{6 \cdot 25}{24} \cdot \frac{4}{5} = \frac{150}{24} \cdot \frac{4}{5} \]
This simplifies to:
\[ \frac{150 \cdot 4}{24 \cdot 5} = \frac{600}{120} = 5 \]
Since both sides are equal, our solution is verified.

### Final Answer
Thus, the value of \( x \) is:
\[ \boxed{\frac{24}{25}} \]