To solve the inequality \( 5x + 7 \leq -8 \), follow these steps:
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Subtract 7 from both sides of the inequality: \[ 5x + 7 - 7 \leq -8 - 7 \] Simplifying this gives: \[ 5x \leq -15 \]
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Divide both sides by 5: \[ x \leq -3 \]
Therefore, the solution to the inequality is: \[ \boxed{x \leq -3} \]