To find the equivalent ratio \( 4:x \) from the ratio \( 12:9 \), we can set up a proportion.
The ratio \( 12:9 \) can be simplified by dividing both numbers by their greatest common divisor (GCD), which is 3:
\[ \frac{12}{9} = \frac{12 \div 3}{9 \div 3} = \frac{4}{3} \]
Now, we have the ratio \( 4:3 \). Next, we will set up the proportion:
\[ \frac{4}{3} = \frac{4}{x} \]
To solve for \( x \), we can cross-multiply:
\[ 4 \cdot x = 4 \cdot 3 \] \[ 4x = 12 \]
Now, divide both sides by 4:
\[ x = 3 \]
Now that we have \( x \), we can write the complete ratio:
\[ 4:3 \]
So, the equivalent ratio of \( 12:9 \) as \( 4:x \) is \( 4:3 \).