https://file.aiquickdraw.com/mathbot/file/1726446233720f4bap4mp.jpg

Let's analyze and solve the three parts of the question from the image you provided:

### a) Write down the smallest possible value of \( n \).

We are given the inequality:
\[
-3 < n \leq 4
\]
Since \( n \) is an integer, the smallest integer that satisfies this inequality is \( -2 \).

**Answer:** \( n = -2 \)

---

### b) What is the inequality shown on the number line?

On the number line:
- The shaded dot at \( -4 \) indicates that \( x = -4 \) is included.
- The open circle at \( 5 \) indicates that \( x = 5 \) is excluded.
- The line is drawn between \( -4 \) and \( 5 \).

This represents the inequality:
\[
-4 \leq x < 5
\]

**Answer:** \( -4 \leq x < 5 \)

---

### c) Solve \( \frac{2}{3}q - 1 > 9 \)

To solve this inequality:
1. Add 1 to both sides:
   \[
   \frac{2}{3}q > 10
   \]
2. Multiply both sides by \( \frac{3}{2} \):
   \[
   q > 15
   \]

**Answer:** \( q > 15 \)

---

Would you like further clarification or details on any of these parts?

Here are 5 related questions to practice:
1. Solve the inequality \( -2 \leq n < 6 \), where \( n \) is an integer.
2. What is the inequality represented by a number line with a closed circle at \( 1 \) and an open circle at \( 6 \)?
3. Solve the inequality \( \frac{3}{4}x + 2 \leq 8 \).
4. If \( -5 < x \leq 2 \), list all integer values of \( x \).
5. Represent the inequality \( -2 < y \leq 4 \) on a number line.

**Tip:** When solving inequalities involving fractions, multiplying both sides by the reciprocal can simplify the process.

Solve the following: 
 a) Write down the smallest possible value of n where -3 < n ≤ 4, and n is an integer. 
 b) What is the inequality shown on the number line between -4 and 5, with a closed circle at -4 and an open circle at 5? 
 c) Solve 2/3q - 1 > 9.

Learn how to solve inequalities such as -3 < n ≤ 4 and interpret inequalities on a number line. This problem covers key mathematical concepts such as number line representation and solving linear inequalities, suitable for students in Grades 6-8.

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