Question: Find the solution set for the inequality -x + 5 ≤ 2.
Options:
x ≥ 3
x ≤ 3
x ≥ 5
x ≤ 5
Correct Answer: x ≤ 3
Solution:
-x + 5 ≤ 2 => -x ≤ -3 => x ≥ 3.
Find the solution set for the inequality -x + 5 ≤ 2.
Practice Questions
Q1
Find the solution set for the inequality -x + 5 ≤ 2.
x ≥ 3
x ≤ 3
x ≥ 5
x ≤ 5
Questions & Step-by-Step Solutions
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.
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