To find the equivalent ratio of 12:9 as 4:x, we can set up a proportion. We will first simplify the ratio 12:9.
The simplified form of 12:9 can be found by dividing both terms by their greatest common divisor, which is 3:
\[ \frac{12}{3} : \frac{9}{3} = 4 : 3 \]
Now we want to set up a proportion with 4:x based on our equivalent ratios:
\[ \frac{4}{3} = \frac{4}{x} \]
To find \(x\), we can cross-multiply:
\[ 4 \cdot x = 4 \cdot 3 \]
Simplifying that gives:
\[ 4x = 12 \]
Now divide both sides by 4:
\[ x = 3 \]
Now we can write the equivalent ratio:
\[ 4 : 3 \]
Thus, the complete ratio is \(4:3\).