Find the solution set for the inequality -x + 5 ≤ 2.

Find the solution set for the inequality -x + 5 ≤ 2.

Correct Answer: x ≥ 3

Step 1: Start with the inequality -x + 5 ≤ 2.
Step 2: To isolate -x, subtract 5 from both sides of the inequality. This gives you -x ≤ 2 - 5.
Step 3: Simplify the right side. 2 - 5 equals -3, so now you have -x ≤ -3.
Step 4: To solve for x, multiply both sides of the inequality by -1. Remember, when you multiply or divide by a negative number, you must flip the inequality sign. This changes -x to x and -3 to 3, giving you x ≥ 3.
Step 5: The solution set is x ≥ 3.

Inequalities – Understanding how to manipulate and solve linear inequalities.
Reversing Inequalities – Recognizing that multiplying or dividing by a negative number reverses the inequality sign.