Question: Solve the inequality -x/2 + 4 > 0. What is the solution?
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?
Practice Questions
Q1
Solve the inequality -x/2 + 4 > 0. What is the solution?
x < 8
x > 8
x < -8
x > -8
Questions & Step-by-Step Solutions
Solve the inequality -x/2 + 4 > 0. What is the solution?
Step 1: Start with the inequality -x/2 + 4 > 0.
Step 2: To isolate -x/2, subtract 4 from both sides. This gives you -x/2 > -4.
Step 3: Now, to get rid of the negative sign in front of x, multiply both sides of the inequality by -2. Remember, when you multiply or divide by a negative number, you must flip the inequality sign. So, -x/2 > -4 becomes x < 8.
Step 4: The solution to the inequality is x < 8.
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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