Question: Find the solution for the inequality: -x + 4 ≤ 2.
Options:
x ≥ 2
x ≤ 2
x ≥ 4
x ≤ 4
Correct Answer: x ≤ 2
Solution:
-x + 4 ≤ 2 => -x ≤ -2 => x ≥ 2.
Find the solution for the inequality: -x + 4 ≤ 2.
Practice Questions
Q1
Find the solution for the inequality: -x + 4 ≤ 2.
x ≥ 2
x ≤ 2
x ≥ 4
x ≤ 4
Questions & Step-by-Step Solutions
Find the solution for the inequality: -x + 4 ≤ 2.
Step 1: Start with the inequality: -x + 4 ≤ 2.
Step 2: To isolate -x, subtract 4 from both sides: -x + 4 - 4 ≤ 2 - 4.
Step 3: This simplifies to: -x ≤ -2.
Step 4: Now, to solve for x, we need to get rid of the negative sign in front of x. Multiply both sides by -1. Remember, when you multiply or divide an inequality by a negative number, you must flip the inequality sign.
Step 5: This gives us: x ≥ 2.
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.
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