Find the value of x in each of the following :
42 : 12 : : 7 : x

Answer

To find the value of \( x \) in the proportion \( 42 : 12 :: 7 : x \), we can set up the equation based on the definition of ratios.

### Step-by-Step Solution:

1. **Set Up the Proportion**:
The given ratio can be expressed as:
\[ \frac{42}{12} = \frac{7}{x} \]

2. **Cross Multiply**:
To eliminate the fractions, we cross multiply:
\[ 42 \cdot x = 12 \cdot 7 \]

3. **Calculate the Right Side**:
Now, calculate \( 12 \cdot 7 \):
\[ 12 \cdot 7 = 84 \]
So, we have:
\[ 42x = 84 \]

4. **Solve for \( x \)**:
To find \( x \), divide both sides by 42:
\[ x = \frac{84}{42} \]

5. **Simplify the Fraction**:
Simplifying \( \frac{84}{42} \):
\[ x = 2 \]

### Final Answer:
The value of \( x \) is \( 2 \).