To solve the inequality \( 5x + 2 \leq -8 \), we start by isolating \( x \).
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Subtract 2 from both sides: \[ 5x + 2 - 2 \leq -8 - 2 \] This simplifies to: \[ 5x \leq -10 \]
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Next, divide both sides by 5: \[ x \leq \frac{-10}{5} \] This simplifies to: \[ x \leq -2 \]
So the solution to the inequality is: \[ \boxed{x \leq -2} \]