To solve the inequality
\[ -10(-5x + 9) \leq 10, \]
let's start by distributing the \(-10\) on the left side:
\[ -10 \times -5x + -10 \times 9 \leq 10. \]
This simplifies to:
\[ 50x - 90 \leq 10. \]
Next, we can add \(90\) to both sides of the inequality:
\[ 50x - 90 + 90 \leq 10 + 90, \]
which simplifies to:
\[ 50x \leq 100. \]
Now, let's divide both sides by \(50\):
\[ x \leq \frac{100}{50}. \]
Thus, we find:
\[ x \leq 2. \]
This means that the solution to the inequality is:
\[ \boxed{(-\infty, 2]}. \]
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