What is the value of x in the proportion x/8 = 3/12?

To find the value of x in the proportion ( \frac{x}{8} = \frac{3}{12} ), we can use cross-multiplication, which is a method effective for solving proportions. In this case, we multiply the numerator of the first fraction by the denominator of the second fraction and set it equal to the product of the denominator of the first fraction and the numerator of the second fraction.

The cross-multiplication gives us:

[ x \cdot 12 = 3 \cdot 8 ]

Simplifying the right side:

[ 3 \cdot 8 = 24 ]

Now our equation looks like this:

[ 12x = 24 ]

To isolate x, we divide both sides by 12:

[ x = \frac{24}{12} ]

Calculating that gives us:

[ x = 2 ]

Thus, the value of x is 2, which corresponds to the correct answer. In this case, x being 2 maintains the equality of the original proportion, as both sides equal ( \frac{2}{8} = \frac{1}{4} ) when simplified, which is equal to ( \frac{3}{12