To use the distributive property to simplify the expression \((-1 + 7 + 9)3x\), we first simplify the expression inside the parentheses:
\[ -1 + 7 + 9 = 6 + 9 = 15. \]
Now, we rewrite the original expression using this result:
\[ 15 \cdot 3x. \]
Next, we can use the distributive property to expand this:
\[ 15 \cdot 3x = (15 \cdot 3)x = 45x. \]
Thus, the equivalent variable expression is:
\[ \boxed{45x}. \]