Question: Solve the inequality -x/2 + 4 > 0. What is the solution set?
Options:
x < 8
x > 8
x ≤ 8
x ≥ 8
Correct Answer: x > 8
Solution:
-x/2 + 4 > 0 => -x/2 > -4 => x < 8.
Solve the inequality -x/2 + 4 > 0. What is the solution set?
Practice Questions
Q1
Solve the inequality -x/2 + 4 > 0. What is the solution set?
x < 8
x > 8
x ≤ 8
x ≥ 8
Questions & Step-by-Step Solutions
Solve the inequality -x/2 + 4 > 0. What is the solution set?
Correct Answer: x < 8
Step 1: Start with the inequality -x/2 + 4 > 0.
Step 2: To isolate -x/2, subtract 4 from both sides: -x/2 > -4.
Step 3: Now, we need to get rid of the negative sign in front of x. To do this, multiply both sides of the inequality by -2. Remember, when you multiply or divide by a negative number, you must flip the inequality sign.
Step 4: After multiplying by -2, the inequality becomes x < 8.
Step 5: The solution set is all values of x that are less than 8.
Inequalities – Understanding how to manipulate and solve linear inequalities.
Algebraic Manipulation – Applying operations to isolate the variable and solve for its value.
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