If * represents a number then the value of * in ` 5(3)/(**) xx 3 (1)/(2) = 19` is :

Options

A. 7
B. 4
C. 6
D. 2

Answer

To solve the equation \( 5(3)/(**) \times 3(1)/(2) = 19 \), we will first replace the symbol \( * \) with a variable \( x \). The equation can be rewritten as:

\[ \frac{5 \cdot 3}{x} \times \frac{3 \cdot 1}{2} = 19 \]

### Step 1: Simplify the left-hand side
First, calculate the multiplication of the fractions:

\[ \frac{5 \cdot 3}{x} \times \frac{3 \cdot 1}{2} = \frac{15}{x} \times \frac{3}{2} \]

Now, multiply the fractions:

\[ \frac{15 \cdot 3}{x \cdot 2} = \frac{45}{2x} \]

### Step 2: Set the equation
Now, we set the left-hand side equal to 19:

\[ \frac{45}{2x} = 19 \]

### Step 3: Cross-multiply
To eliminate the fraction, we can cross-multiply:

\[ 45 = 19 \cdot 2x \]

This simplifies to:

\[ 45 = 38x \]

### Step 4: Solve for \( x \)
Now, divide both sides by 38 to isolate \( x \):

\[ x = \frac{45}{38} \]

### Step 5: Simplify \( x \)
To simplify \( \frac{45}{38} \):

Since 45 and 38 have no common factors, we can leave it as is. However, we can also express it as a decimal:

\[ x \approx 1.1842 \]

### Step 6: Conclusion
The value of \( * \) is approximately \( 1.1842 \).

However, if we consider the context of the problem, we might be looking for a whole number. Therefore, we can check if \( x = 7 \) satisfies the original equation.

### Verification
Substituting \( x = 7 \):

\[ \frac{5 \cdot 3}{7} \times \frac{3}{2} = \frac{15}{7} \times \frac{3}{2} = \frac{45}{14} \]

Now, we check if this equals 19:

\[ \frac{45}{14} \approx 3.2143 \quad \text{(not equal to 19)} \]

Thus, we conclude that \( x = 7 \) is not correct, and we stick with \( x = \frac{45}{38} \).

### Final Answer
The value of \( * \) is \( \frac{45}{38} \) or approximately \( 1.1842 \).