Let's solve the proportion step by step.
We start with the given proportion:
[tex]\[
\frac{x}{6} = \frac{36}{24}
\][/tex]
To find the value of [tex]\( x \)[/tex], we can use cross-multiplication. Cross-multiplication involves multiplying the numerator of one fraction by the denominator of the other fraction and setting the two products equal. That is, we multiply [tex]\( x \)[/tex] by 24 and 6 by 36:
[tex]\[
x \cdot 24 = 6 \cdot 36
\][/tex]
Next, let's simplify the right-hand side:
[tex]\[
x \cdot 24 = 216
\][/tex]
To solve for [tex]\( x \)[/tex], we need to isolate [tex]\( x \)[/tex]. We do this by dividing both sides of the equation by 24:
[tex]\[
x = \frac{216}{24}
\][/tex]
When we perform the division:
[tex]\[
x = 9
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] that makes the proportion true is:
[tex]\[
\boxed{9}
\][/tex]
