Add 5 to both sides: Add 5 to both sides of the inequality to isolate x on one side. x - 5 + 5 <= 2 + 5Simplify inequality: Simplify both sides of the inequality. x <= 7Check solution: Check the solution by choosing a number less than or equal to 7 and substituting it back into the original inequality to see if it holds true. Let's choose x = 6. 6 - 5 <= 2 1 <= 2, which is true.Write final answer: Write the final answer and conclude the solution. The solution set for the inequality x - 5 <= 2 is all real numbers less than or equal to 7.

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$x-5 \leq 2$

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x-5 \leq 2

Add $5$ to both sides: Add $5$ to both sides of the inequality to isolate $x$ on one side. $\newline$ $x - 5 + 5 \leq 2 + 5$
Simplify inequality: Simplify both sides of the inequality. $x \leq 7$
Check solution: Check the solution by choosing a number less than or equal to $7$ and substituting it back into the original inequality to see if it holds true. $\newline$ Let's choose $x = 6$ . $\newline$ $6 - 5 \leq 2$ $\newline$ $1 \leq 2$ , which is true.
Write final answer: Write the final answer and conclude the solution. $\newline$ The solution set for the inequality $x - 5 \leq 2$ is all real numbers less than or equal to $7$ .