To determine the value of [tex]\( x \)[/tex] that makes the proportion [tex]\(\frac{x}{6} = \frac{36}{24}\)[/tex] true, let's go through the steps methodically.
1. Write down the original proportion:
[tex]\[
\frac{x}{6} = \frac{36}{24}
\][/tex]
2. Simplify the right-hand side:
Notice that [tex]\( \frac{36}{24} \)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 12.
[tex]\[
\frac{36 \div 12}{24 \div 12} = \frac{3}{2}
\][/tex]
So, the proportion simplifies to:
[tex]\[
\frac{x}{6} = \frac{3}{2}
\][/tex]
3. Solve for [tex]\( x \)[/tex] using cross-multiplication:
Cross-multiplication involves multiplying the numerator of one fraction by the denominator of the other fraction:
[tex]\[
x \cdot 2 = 3 \cdot 6
\][/tex]
Simplify:
[tex]\[
2x = 18
\][/tex]
4. Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{18}{2} = 9
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] that makes the proportion true is [tex]\(\boxed{9}\)[/tex]. This corresponds to option B.
