Question: Solve the inequality -4x + 8 ≤ 0. What is the solution?
Options:
x < 2
x > 2
x ≤ 2
x ≥ 2
Correct Answer: x ≤ 2
Solution:
-4x + 8 ≤ 0 => -4x ≤ -8 => x ≥ 2.
Solve the inequality -4x + 8 ≤ 0. What is the solution?
Practice Questions
Q1
Solve the inequality -4x + 8 ≤ 0. What is the solution?
x < 2
x > 2
x ≤ 2
x ≥ 2
Questions & Step-by-Step Solutions
Solve the inequality -4x + 8 ≤ 0. What is the solution?
Correct Answer: x ≥ 2
Step 1: Start with the inequality -4x + 8 ≤ 0.
Step 2: To isolate the term with x, subtract 8 from both sides. This gives you -4x ≤ -8.
Step 3: Now, divide both sides by -4. Remember, when you divide by a negative number, you must flip the inequality sign. So, -8 divided by -4 becomes 2, and the inequality changes direction: x ≥ 2.
Step 4: The solution to the inequality is x ≥ 2.
Inequalities – Understanding how to manipulate and solve linear inequalities.
Algebraic Manipulation – Applying operations to isolate the variable and reverse the inequality sign when multiplying or dividing by a negative number.
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