https://file.aiquickdraw.com/mathbot/file/1727369456318g2och6rk.jpg

From the image, it appears that there are two problems where the interval and inequality notations have been entered incorrectly. Let’s address both issues:

### a) **Enter \([3, ∞)\) in interval notation**
- The correct interval notation for the expression \([3, ∞)\) is:
  \[
  [3, \infty)
  \]
  Where:
  - The square bracket "[" means 3 is included in the interval.
  - The parenthesis ")" after ∞ means the interval goes infinitely and does not include infinity (as infinity is not a real number that can be included).

### Mistake in your answer:
You entered:
\[
3 < x
\]
This is inequality notation, not interval notation. To express this in correct interval notation, write \([3, \infty)\).

---

### b) **Enter \(2 < x \leq 7\) in inequality notation**
- The correct inequality notation for the interval \( (2, 7] \) is:
  \[
  2 < x \leq 7
  \]
  Where:
  - The inequality "2 < x" indicates that \(x\) is strictly greater than 2 (not including 2).
  - The inequality "\(x \leq 7\)" means \(x\) is less than or equal to 7 (7 is included).

### Mistake in your answer:
You entered:
\[
(2, 7]
\]
This is interval notation. To express this in correct inequality notation, use \(2 < x \leq 7\).

---

Would you like more details or have any questions? Here are some related questions for further practice:

1. What is the interval notation for \(x > 5\)?
2. How do you express the interval \((-∞, 0]\) in inequality form?
3. What is the inequality notation for \(x \in (-3, 8)\)?
4. How do you write \(x \leq -2\) in interval notation?
5. Convert the interval notation \([0, 4)\) into an inequality.

**Tip:** Interval notation uses brackets to show whether endpoints are included or excluded, whereas inequality notation uses comparison symbols like \(<\), \(>\), \(≤\), and \(≥\).

a) Enter [3, ∞) in interval notation.
b) Enter 2 < x ≤ 7 in inequality notation.

Learn how to convert between interval notation and inequality notation. This example explains the differences between [3, ∞) and 3 < x, as well as (2, 7] and 2 < x ≤ 7. Suitable for students in Grades 6-8, focusing on real number line representations.

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