\( \xrightarrow{\text { Graph the solution set for this inequality on the number line: } 5(x-3)+2 \leq 2(x-5)} \)

To solve the inequality \( 5(x-3)+2 \leq 2(x-5) \), start by expanding both sides. This gives you \( 5x - 15 + 2 \leq 2x - 10 \), which simplifies to \( 5x - 13 \leq 2x - 10 \). Next, bring all terms involving \( x \) to one side and constant terms to the other side: \( 5x - 2x \leq -10 + 13 \), which results in \( 3x \leq 3 \). Dividing by 3 yields \( x \leq 1 \). On a number line, you would represent this solution by shading all points to the left of (and including) 1, with a closed circle at 1. If you’re new to inequalities, it’s easy to make a common mistake by flipping the inequality sign when multiplying or dividing by a negative number. Always keep an eye on the sign of the number you’re working with! And remember to check your inequality by substituting a value from the solution set, like \( x = 0 \), back into the original inequality to ensure it holds true.