To solve the proportion [tex]\(\frac{x}{6} = \frac{36}{24}\)[/tex], follow these steps:
1. Simplify the right-hand side of the equation:
[tex]\[
\frac{36}{24}
\][/tex]
By dividing both the numerator and the denominator by their greatest common divisor (which is 12), we get:
[tex]\[
\frac{36 \div 12}{24 \div 12} = \frac{3}{2}
\][/tex]
2. Rewrite the proportion using the simplified right-hand side:
[tex]\[
\frac{x}{6} = \frac{3}{2}
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
To find [tex]\(x\)[/tex], cross-multiply the fractions:
[tex]\[
x \times 2 = 6 \times 3
\][/tex]
4. Perform the multiplication:
[tex]\[
2x = 18
\][/tex]
5. Isolate [tex]\(x\)[/tex] by dividing both sides by 2:
[tex]\[
x = \frac{18}{2} = 9
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] that makes the proportion true is:
[tex]\[
\boxed{9}
\][/tex]
