Determine the solution set for the inequality 5 - x ≥ 2.
Practice Questions
Q1
Determine the solution set for the inequality 5 - x ≥ 2.
x ≤ 3
x < 3
x ≥ 3
x > 3
Questions & Step-by-Step Solutions
Determine the solution set for the inequality 5 - x ≥ 2.
Correct Answer: x ≤ 3
Step 1: Start with the inequality 5 - x ≥ 2.
Step 2: To isolate -x, subtract 5 from both sides. 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 all values of x that are less than or equal to 3.
Inequalities – Understanding how to manipulate and solve inequalities, including reversing the inequality sign when multiplying or dividing by a negative number.
Algebraic Manipulation – Skills in rearranging equations and isolating variables to find solutions.
