Answer :
To determine what value of [tex]\( x \)[/tex] makes the proportion [tex]\(\frac{x}{6} = \frac{36}{24}\)[/tex] true, we follow these steps:
1. Identify the proportion:
[tex]\[ \frac{x}{6} = \frac{36}{24} \][/tex]
2. Cross-multiply to eliminate the fractions:
[tex]\[ x \cdot 24 = 36 \cdot 6 \][/tex]
3. Perform the multiplication on each side:
[tex]\[ x \cdot 24 = 216 \][/tex]
4. Solve for [tex]\( x \)[/tex] by dividing both sides of the equation by 24:
[tex]\[ x = \frac{216}{24} \][/tex]
5. Simplify the division:
[tex]\[ x = 9 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] that makes the proportion true is [tex]\( \boxed{9} \)[/tex]. Thus, the correct answer is [tex]\( A \)[/tex].
1. Identify the proportion:
[tex]\[ \frac{x}{6} = \frac{36}{24} \][/tex]
2. Cross-multiply to eliminate the fractions:
[tex]\[ x \cdot 24 = 36 \cdot 6 \][/tex]
3. Perform the multiplication on each side:
[tex]\[ x \cdot 24 = 216 \][/tex]
4. Solve for [tex]\( x \)[/tex] by dividing both sides of the equation by 24:
[tex]\[ x = \frac{216}{24} \][/tex]
5. Simplify the division:
[tex]\[ x = 9 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] that makes the proportion true is [tex]\( \boxed{9} \)[/tex]. Thus, the correct answer is [tex]\( A \)[/tex].
