To solve the inequality \( -2(-10x + 5) \leq 3 \), we will first simplify the left side.
Start by distributing the \(-2\):
\[ -2(-10x) + (-2)(5) \leq 3 \]
This simplifies to:
\[ 20x - 10 \leq 3 \]
Next, add \(10\) to both sides of the inequality:
\[ 20x - 10 + 10 \leq 3 + 10 \]
This gives:
\[ 20x \leq 13 \]
Now, divide both sides by \(20\):
\[ x \leq \frac{13}{20} \]
Thus, the solution to the inequality is:
\[ x \leq \frac{13}{20} \]