To solve the inequality \( 5x + 8 \leq -3 \), follow these steps:
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Isolate the term with \( x \): Subtract \( 8 \) from both sides.
\[ 5x + 8 - 8 \leq -3 - 8 \]
This simplifies to:
\[ 5x \leq -11 \]
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Solve for \( x \): Divide both sides by \( 5 \).
\[ x \leq \frac{-11}{5} \]
Simplifying \( \frac{-11}{5} \) gives:
\[ x \leq -2.2 \]
So the solution to the inequality is:
\[ x \leq -2.2 \]