To determine the value of [tex]\( x \)[/tex] such that the fractions [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{12}{x}\)[/tex] are equivalent, we need to set up an equation based on the equality of the fractions. Here’s the detailed step-by-step process:
1. Write down the equivalence of the fractions:
[tex]\[
\frac{3}{4} = \frac{12}{x}
\][/tex]
2. To eliminate the fractions, use cross-multiplication. This method involves multiplying the numerator of one fraction by the denominator of the other fraction and setting the products equal to each other:
[tex]\[
3 \times x = 4 \times 12
\][/tex]
3. Perform the multiplication on the right-hand side:
[tex]\[
3x = 48
\][/tex]
4. To solve for [tex]\( x \)[/tex], divide both sides of the equation by 3:
[tex]\[
x = \frac{48}{3}
\][/tex]
5. Simplify the division to find the value of [tex]\( x \)[/tex]:
[tex]\[
x = 16
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] that makes the fractions [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{12}{x}\)[/tex] equivalent is [tex]\( 16 \)[/tex].
Hence, the correct answer is:
D. 16
