To solve the inequality \( x + 5 \leq 13 \), you need to isolate \( x \). Here are the steps:
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Subtract 5 from both sides of the inequality: \[ x + 5 - 5 \leq 13 - 5 \]
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This simplifies to: \[ x \leq 8 \]
So the solution to the inequality is \( x \leq 8 \).
In interval notation, this solution is expressed as \( (-\infty, 8] \).