To solve the inequality \( 16x - 35 \leq 13 \), follow these steps:
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Add 35 to both sides to isolate the term with \( x \):
\[ 16x - 35 + 35 \leq 13 + 35 \]
Simplifying this gives:
\[ 16x \leq 48 \]
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Divide both sides by 16 to solve for \( x \):
\[ x \leq \frac{48}{16} \]
Simplifying the right side gives:
\[ x \leq 3 \]
Thus, the solution to the inequality is:
\[ \boxed{x \leq 3} \]