You only get only one try for the answer; please draw the graph. a. Choose the correct interval notation for the inequality notation
x > −3

[-3, ∞)

(-3, ∞)

(-∞ , -3)

(-∞ , 3)
None of these

b. Choose the correct interval notation for the inequality notation
−3 < x ≤ 3 or 7 ≤ x

(-3, 3] ⋃ [7, ∞)

(-3, 3) ⋃ (7, ∞)

[-3, 3) ⋃ [7, ∞)

[-3, 3] ⋃ (7, ∞)
None of these

c. Choose the correct interval notation for the inequality notation
x ≤ −3 or 7 ≤ x

(-∞ , -3] ⋃ (7, ∞)

(-∞ , -3) ⋃ (7, ∞)

(-∞ , -3] ⋃ [7, ∞)

(-∞ , 3) ⋃ (7, ∞)
None of these

Here is the graph displaying the interval notations for the three inequalities. Let me know if you'd like any further clarifications or details!

1. The correct interval for **x > -3** is **(-3, ∞)**.
2. The correct interval for **-3 < x ≤ 3 or 7 ≤ x** is **(-3, 3] ⋃ [7, ∞)**.
3. The correct interval for **x ≤ -3 or 7 ≤ x** is **(-∞, -3] ⋃ [7, ∞)**.

Would you like to go into more detail or ask any questions?

### Follow-up Questions:
1. What is the difference between open and closed intervals?
2. How do you graph inequalities involving two or more intervals?
3. Can you explain union (⋃) of intervals and how it works?
4. What happens when two intervals overlap?
5. How do you solve a compound inequality like **x > -3 and x ≤ 5**?

**Tip:** Open intervals exclude the boundary values, while closed intervals include them.

You only get only one try for the answer; please draw the graph. a. Choose the correct interval notation for the inequality notation x > −3 [-3, ∞) (-3, ∞) (-∞ , -3) (-∞ , 3) None of these b. Choose the correct interval notation for the inequality notation −3 < x ≤ 3 or 7 ≤ x (-3, 3] ⋃ [7, ∞) (-3, 3) ⋃ (7, ∞) [-3, 3) ⋃ [7, ∞) [-3, 3] ⋃ (7, ∞) None of these c. Choose the correct interval notation for the inequality notation x ≤ −3 or 7 ≤ x (-∞ , -3] ⋃ (7, ∞) (-∞ , -3) ⋃ (7, ∞) (-∞ , -3] ⋃ [7, ∞) (-∞ , 3) ⋃ (7, ∞) None of these

Explore how to express inequalities in interval notation. Learn the differences between open and closed intervals with examples such as x > -3, -3 < x ≤ 3 or 7 ≤ x, and x ≤ -3 or 7 ≤ x. Ideal for students in Grades 9-11.

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