Find the solution set for the inequality -x + 4 < 2.

Find the solution set for the inequality -x + 4 < 2.

Correct Answer: x > 2

Step 1: Start with the inequality -x + 4 < 2.
Step 2: To isolate -x, subtract 4 from both sides. This gives you -x < 2 - 4.
Step 3: Simplify the right side. 2 - 4 equals -2, so now you have -x < -2.
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. So, -x < -2 becomes x > 2.
Step 5: The solution set is all values of x that are greater than 2.

Inequalities – Understanding how to manipulate and solve linear inequalities.
Reversing Inequalities – Recognizing that when multiplying or dividing by a negative number, the direction of the inequality changes.