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Part 1
Solve the linear inequality. Other than empty set​, graph the solution set on a number line.
4 minus StartFraction x Over 2 EndFraction greater than 8

Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The solution set in interval notation is 
  
enter your response here.
​(Simplify your answer. Use integers or fractions for any numbers in the expression. Type your answer in interval​ notation.)
B.
The solution set is empty set

Let's solve the linear inequality step by step.

### Given inequality:
\[
4 - \frac{x}{2} > 8
\]

### Step 1: Isolate the variable term

Subtract \(4\) from both sides:
\[
4 - \frac{x}{2} - 4 > 8 - 4
\]
\[
-\frac{x}{2} > 4
\]

### Step 2: Eliminate the fraction

To eliminate the fraction, multiply both sides by \(-2\). Keep in mind that multiplying by a negative number reverses the inequality sign:
\[
x < -8
\]

### Solution in interval notation:
The solution set is all numbers less than \(-8\), which in interval notation is:
\[
(-\infty, -8)
\]

### Final Answer:
A. The solution set in interval notation is \((- \infty, -8)\).

Would you like a graph of this solution on a number line? Feel free to ask any questions or request more details!

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Here are five related questions for further practice:
1. How would the inequality change if it were \(4 + \frac{x}{2} > 8\)?
2. Solve the inequality \(2 - \frac{x}{3} \leq 5\).
3. What happens when you multiply or divide an inequality by a negative number?
4. Can you solve the inequality \(5 - \frac{3x}{4} > 7\)?
5. How do you graph solutions involving intervals on the number line?

**Tip:** Always remember to reverse the inequality sign when multiplying or dividing by a negative number!

Solve the linear inequality. Other than empty set​, graph the solution set on a number line. 4 minus StartFraction x Over 2 EndFraction greater than 8. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. A. The solution set in interval notation is ___. (Simplify your answer. Use integers or fractions for any numbers in the expression. Type your answer in interval notation.) B. The solution set is empty set.

Learn how to solve the linear inequality 4 - x/2 > 8 with a detailed step-by-step solution. This problem covers key algebraic concepts, including solving inequalities, reversing the inequality sign, and expressing the solution in interval notation. Suitable for students in Grades 7-10.

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