if 3, x, 6, 12 ar in proportion , then x =

Explanation

To solve the problem where 3, x, 6, and 12 are in proportion, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Proportion**: When we say that four numbers are in proportion, it means that the ratio of the first two numbers is equal to the ratio of the last two numbers. Mathematically, this can be expressed as:
\[ \frac{3}{x} = \frac{6}{12} \]

2. **Cross Multiplication**: To solve for x, we can use cross multiplication. This means we will multiply the numerator of the first fraction by the denominator of the second fraction and set it equal to the numerator of the second fraction multiplied by the denominator of the first fraction:
\[ 3 \times 12 = x \times 6 \]

3. **Calculating the Left Side**: Now, we calculate the left side of the equation:
\[ 3 \times 12 = 36 \]
So, we have:
\[ 36 = x \times 6 \]

4. **Isolating x**: To find the value of x, we need to isolate it. We can do this by dividing both sides of the equation by 6:
\[ x = \frac{36}{6} \]

5. **Final Calculation**: Now we perform the division:
\[ x = 6 \]

### Final Answer:
Thus, the value of x is **6**.

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