Question

Solve each inequality​ analytically, writing the solution set in interval notation. Support your answer graphically.​ (Hint: Once part ​(a) is​ done, part ​(b) follows from the answer to part ​(a)​.) ​(a) 9−​(x+4​)<0 ​(b) 9−​(x+4​)≥0 Question content area bottom Part 1 ​(a) The solution set of 9−​(x+4​)<0 is enter your response here. ​(Type your answer in interval​ notation.)

Answer 1

Part (a)

`9-(x+4)<0 \\ \\ 9<x+4 \\ \\ 5<x \\ \\ \boxed{x \in (5, \infty)}`

Part (b)

`x \in (-\infty, 5]`

Answer 2

The solution set for 9 - (x + 4) < 0 is x > 5, and for 9 - (x + 4) ≥ 0, it is x ≥ 5. Both solutions are represented in interval notation as (5, ∞).

To solve the inequality 9 - (x + 4) < 0, follow these steps:

1. Simplify the expression inside the parentheses: 9 - x - 4 < 0.

2. Combine like terms: 5 - x < 0.

3. Subtract 5 from both sides: -x < -5.

4. Multiply both sides by -1 (since multiplying or dividing by a negative number flips the inequality sign): x > 5.

So, the solution set for the inequality 9 - (x + 4) < 0 is x > 5.

For part (b), the inequality is 9 - (x + 4) ≥ 0. Using the solution from part (a), since x > 5, the solution for part (b) is x ≥ 5.

Therefore, the solution set for (a) is x > 5, and for (b) is x ≥ 5, both expressed in interval notation as (5, ∞).