To find the value of \( x \) in the equivalent ratio \( 4:x \) based on the ratio \( 12:9 \), we can start by simplifying the ratio \( 12:9 \).
First, we can simplify \( 12:9 \) by dividing both terms by their greatest common divisor, which is 3:
\[ 12 \div 3 = 4 \] \[ 9 \div 3 = 3 \]
So, the simplified ratio \( 12:9 \) is \( 4:3 \).
Now, we want to write \( 4:x \) as equivalent to \( 4:3 \). Since both ratios are equivalent, we can set them equal to each other:
\[ \frac{4}{x} = \frac{4}{3} \]
To find \( x \), we can cross-multiply:
\[ 4 \cdot 3 = 4 \cdot x \] \[ 12 = 4x \]
Now, divide both sides by 4:
\[ x = \frac{12}{4} = 3 \]
Now we have the value of \( x \). Therefore, the ratio \( 4:x \) can be written as:
\[ 4:3 \]
Hence, the equivalent ratio of \( 12:9 \) as \( 4:x \) is:
\[ 4:3 \]