To determine whether the equation \(-12w + 15 = 2(-6w + 9) - 3\) has one solution, no solution, or infinitely many solutions, we will first simplify the right-hand side of the equation.
Starting with the right-hand side:
\[ 2(-6w + 9) - 3 \]
Distributing the \(2\):
\[ = -12w + 18 - 3 \]
Now, simplifying:
\[ = -12w + 15 \]
Now we rewrite the original equation with our simplified right side:
\[ -12w + 15 = -12w + 15 \]
Both sides of the equation are identical. This means that for every value of \(w\), the equation holds true. Thus, the equation has infinitely many solutions.
In summary, the answer is:
Infinitely many solutions.
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