To solve the equation \( x + 3 = 1.5 \cdot (x - 9 - 3) \), let's simplify it step by step.
Start with the original equation:
\[ x + 3 = 1.5 \cdot (x - 9 - 3) \]
Simplify the right side inside the parentheses:
\[ x - 9 - 3 = x - 12 \]
So the equation becomes:
\[ x + 3 = 1.5 \cdot (x - 12) \]
Now distribute \(1.5\) on the right side:
\[ x + 3 = 1.5x - 18 \]
Now, rearrange the equation to get all terms involving \(x\) on one side and constant terms on the other side. Let's subtract \(1.5x\) from both sides:
\[ x - 1.5x + 3 = -18 \]
This simplifies to:
\[ -0.5x + 3 = -18 \]
Next, subtract \(3\) from both sides:
\[ -0.5x = -18 - 3 \]
This gives:
\[ -0.5x = -21 \]
Now, divide both sides by \(-0.5\):
\[ x = \frac{-21}{-0.5} = 21 \div 0.5 = 42 \]
The solution to the equation is:
\[ \boxed{42} \]