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The problem involves solving two inequalities analytically and expressing the solution in interval notation:

### Problem:
Solve each inequality analytically, writing the solution set in interval notation.
- (a) \( 6 - (x + 4) < 0 \)
- (b) \( 6 - (x + 4) \geq 0 \)

The hint suggests that part (b) can be solved based on part (a)'s answer.

### Solution:

#### Part (a): \( 6 - (x + 4) < 0 \)
1. Simplify the expression:
   \[
   6 - (x + 4) = 6 - x - 4 = 2 - x
   \]
   So the inequality becomes:
   \[
   2 - x < 0
   \]
2. Solve for \( x \):
   \[
   2 < x
   \]
   Which means:
   \[
   x > 2
   \]
3. The solution set for part (a) in interval notation is:
   \[
   (2, \infty)
   \]

#### Part (b): \( 6 - (x + 4) \geq 0 \)
1. From part (a), we already simplified \( 6 - (x + 4) \) to \( 2 - x \), so the inequality becomes:
   \[
   2 - x \geq 0
   \]
2. Solve for \( x \):
   \[
   2 \geq x
   \]
   Which means:
   \[
   x \leq 2
   \]
3. The solution set for part (b) in interval notation is:
   \[
   (-\infty, 2]
   \]

### Final Answer:
- Part (a): \( (2, \infty) \)
- Part (b): \( (-\infty, 2] \)

Would you like further details on how to graph these solutions?

Here are 5 related questions for practice:
1. How do you graph inequalities like \( x > 2 \) on a number line?
2. What is the difference between strict inequalities (<, >) and non-strict inequalities (≤, ≥)?
3. How can we check if a specific value satisfies an inequality?
4. Can inequalities have more than one solution? If so, how do you combine the solutions?
5. What happens to the inequality sign when you multiply or divide by a negative number?

**Tip**: When solving inequalities, always remember to reverse the inequality sign when multiplying or dividing by a negative number.

Solve each inequality analytically, writing the solution set in interval notation. (a) 6 - (x + 4) < 0, (b) 6 - (x + 4) ≥ 0

Learn how to solve linear inequalities such as 6 - (x + 4) < 0 and 6 - (x + 4) ≥ 0 using interval notation. This solution covers algebraic concepts, interval notation, and inequalities. Suitable for students in Grades 8-10.

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