To solve the equation \( 3(4x + 3) = 4x + \text{blank} \cdot x + 9 \), we first simplify the left side.
Distributing the 3 on the left side: \[ 3(4x + 3) = 12x + 9 \]
Now, we have: \[ 12x + 9 = 4x + \text{blank} \cdot x + 9 \]
Next, we can simplify the equation by subtracting 9 from both sides: \[ 12x = 4x + \text{blank} \cdot x \]
Now, we can isolate the \(x\) terms on one side. First, subtract \(4x\) from both sides: \[ 12x - 4x = \text{blank} \cdot x \] \[ 8x = \text{blank} \cdot x \]
To find the value for "blank," we can set the coefficients of \(x\) equal to each other: \[ 8 = \text{blank} \]
Therefore, the value that fills the blank is: \[ \text{blank} = 8 \]
Thus, the complete equation is: \[ 3(4x+3) = 4x + 8x + 9 \]