https://file.aiquickdraw.com/mathbot/file/17268202959522h1myzly.jpg

In the image, we are asked to identify the correct inequality that matches the number line diagram. Let's break it down:

1. **Closed circle on -3**: This indicates that the value at -3 is included in the solution set. Therefore, \( x \geq -3 \) (or \( x \leq -3 \)) should be part of the inequality.
   
2. **Open circle on 2**: This indicates that the value at 2 is not included in the solution set, so \( x < 2 \) should be part of the inequality.

Thus, the solution is the inequality that includes \( -3 \leq x < 2 \), since the value of \( x \) can be equal to -3 but less than 2.

### Answer: The correct inequality is **(d) \(-3 \leq x < 2\)**.

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Would you like further explanation on inequalities or this particular solution?

Here are 5 related questions to expand your understanding:

1. What is the difference between an open and a closed circle on a number line?
2. How do you graph inequalities on a number line?
3. What does it mean when an inequality includes "less than" or "greater than" without "equal to"?
4. Can you give an example of a compound inequality and solve it?
5. How would this inequality change if the open circle were on -3 and the closed circle on 2?

**Tip**: Always remember, a closed circle on a number line means the value is included (≤ or ≥), while an open circle means it is not (< or >).

Hvilken ulighed passer til tegningen? (a) -3 ≤ x ≤ 2, b) -3 < x < 2, c) -3 < x ≤ 2, d) -3 ≤ x < 2

Learn how to solve inequalities with number lines by identifying the correct inequality. This problem, suitable for Grades 6-8, covers how closed and open circles on a number line represent inequalities.

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