Students Amber and Alfie evaluate inequalities on number lines, marking correct answers with a tick or incorrect ones with a cross.

Let’s go through each question one by one. We’ll check what the number line shows, then compare it to Amber’s and Alfie’s answers to see who is correct (tick) or wrong (trash).

Remember:
- A closed circle (●) means “include this number” → use ≤ or ≥
- An open circle (○) means “do NOT include this number” → use < or >
- An arrow pointing right means “greater than”
- An arrow pointing left means “less than”
- Two circles with a line between them mean “between two numbers”

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Question 1:
Number line: Closed circle at -1, arrow going right → x ≥ -1
Amber says: x = -1 → ✘ Wrong (only one point, not all values ≥ -1)
Alfie says: x ≥ -1 → ✔ Correct

→ Amber: Trash | Alfie: Tick

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Question 2:
Number line: Arrow from left up to closed circle at 2 → x ≤ 2
Amber says: x < 2 → ✘ Wrong (misses the equal part — circle is closed!)
Alfie says: x ≤ 2 → ✔ Correct

→ Amber: Trash | Alfie: Tick

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Question 3:
Number line: Open circle at -3, arrow going right → x > -3
Amber says: x < -3 → ✘ Wrong (direction is opposite!)
Alfie says: x > -3 → ✔ Correct

→ Amber: Trash | Alfie: Tick

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Question 4:
Number line: Closed circle at 0, arrow going right → x ≥ 0
Amber says: x > 0 → ✘ Wrong (misses the equal — circle is closed!)
Alfie says: x = 0 → ✘ Wrong (only one point, but arrow goes right — should be all values ≥ 0)

Wait — actually, looking again: both are wrong? But let’s double-check.

The number line has a closed circle at 0 and an arrow to the right → that means x ≥ 0.

Amber said x > 0 → misses 0 → wrong
Alfie said x = 0 → only includes 0, not everything after → also wrong

But in the worksheet, Amber’s box is green (correct?) and Alfie’s is white? Wait — no, in the image, for Q4, Amber’s answer is highlighted green, meaning she’s marked correct? That can’t be right...

Hold on — maybe I misread the number line.

Looking again at Q4: It’s a closed circle at 0, and the line goes to the right → definitely x ≥ 0.

Amber wrote: x > 0 → which would be open circle at 0 → so incorrect.

Alfie wrote: x = 0 → which is just the point → also incorrect.

But in the original image, Amber’s answer is colored green — perhaps there’s a mistake in the worksheet? Or maybe I’m misseeing?

Wait — let me re-express:

Actually, looking carefully at the image provided: In row 4, Amber’s answer “x > 0” is in a GREEN box, and Alfie’s “x = 0” is in a WHITE box. But according to math, NEITHER is correct — it should be x ≥ 0.

This suggests either:
- The worksheet has an error, OR
- I’m misreading the number line.

Wait — look again: Is the circle really closed? Yes, it’s filled in. So it must include 0.

Therefore, correct answer is x ≥ 0.

So Amber (x > 0) → trash
Alfie (x = 0) → trash

But since the worksheet marks Amber as correct (green), maybe we’re supposed to follow what’s shown? No — our job is to solve accurately.

I think there might be a typo in the worksheet. Based on standard math rules:

✔ Correct inequality: x ≥ 0
✘ Amber: x > 0 → trash
✘ Alfie: x = 0 → trash

But since the problem says “tick or trash their answers”, and based on accuracy, both are wrong.

However, let’s continue and come back if needed.

Actually — wait! Maybe in Q4, the number line is ONLY the point at 0? No, it clearly has an arrow to the right.

I think we have to go with math truth: both are wrong. But since the worksheet highlights Amber as correct, perhaps it’s a trick? Or maybe I need to accept that for now and move on.

Alternatively — perhaps the arrow is not there? Let me visualize again.

In the user’s image description, for Q4: “closed circle at 0, arrow to the right” → yes.

So I will mark both as wrong. But let’s note that.

For now, proceed.

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Question 5:
Number line: Arrow from left to closed circle at 4 → x ≤ 4
Amber says: x ≥ 4 → ✘ Wrong (opposite direction)
Alfie says: x ≤ 4 → ✔ Correct

→ Amber: Trash | Alfie: Tick

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Question 6:
Number line: Open circle at -2, open circle at 3, line between → -2 < x < 3
Amber says: -2 < x < 3 → ✔ Correct
Alfie says: x < 3 → ✘ Wrong (doesn’t mention lower bound)

→ Amber: Tick | Alfie: Trash

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Question 7:
Number line: Open circle at -5, closed circle at -1, line between → -5 < x ≤ -1
Amber says: -5 < x ≤ -1 → ✔ Correct
Alfie says: -5 ≤ x < -1 → ✘ Wrong (circles are swapped — he included -5 and excluded -1, but it’s the opposite)

→ Amber: Tick | Alfie: Trash

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Question 8:
Number line: Open circle at -4, open circle at 2, line between → -4 < x < 2
Amber says: -4 < x ≤ 2 → ✘ Wrong (she included 2, but circle is open)
Alfie says: -4 < x < 2 → ✔ Correct

→ Amber: Trash | Alfie: Tick

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Question 9:
Number line: Closed circle at -4, closed circle at 1, line between → -4 ≤ x ≤ 1
Amber says: -4 ≤ x ≤ 1 → ✔ Correct
Alfie says: -4 ≤ x ≤ 0 → ✘ Wrong (upper limit is 1, not 0)

→ Amber: Tick | Alfie: Trash

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Question 10:
Number line: Closed circle at 0, open circle at 1, line between → 0 ≤ x < 1
Amber says: 0 < x < 1 → ✘ Wrong (excludes 0, but circle is closed)
Alfie says: 0 ≤ x < 1 → ✔ Correct

→ Amber: Trash | Alfie: Tick

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Now, going back to Question 4 — let’s resolve it.

In Q4: Number line shows closed circle at 0, arrow to the right → x ≥ 0

Amber: x > 0 → this excludes 0 → incorrect
Alfie: x = 0 → only the point → incorrect

But in the worksheet, Amber’s answer is colored green — which might indicate the worksheet considers her correct. However, mathematically, she is not.

Perhaps there’s a misprint? Or maybe the circle is meant to be open? But it’s drawn closed.

Given that, I think we must go with mathematical accuracy.

So for Q4: Both are wrong.

But let’s check the pattern — in other questions, when the circle is closed, they use ≤ or ≥.

So for consistency, Q4 should be x ≥ 0.

Thus:

Amber: x > 0 → trash
Alfie: x = 0 → trash

But since the problem asks to tick or trash *their* answers, and neither matches, both get trash.

However, looking at the original image again (as described), in row 4, Amber’s box is green — which might mean the worksheet intends for her to be correct. But that would be a mistake.

To stay true to math, I’ll mark both as wrong.

But let’s see — perhaps in some contexts, x > 0 is accepted if the circle is closed? No, that’s not standard.

I think it’s safer to assume the worksheet has an error in Q4, and we correct it.

Final decision for Q4: Both incorrect.

But to match the format, let’s list all:

Summary:

Q1: Amber ✘, Alfie ✔
Q2: Amber ✘, Alfie ✔
Q3: Amber ✘, Alfie ✔
Q4: Amber ✘, Alfie ✘ [but worksheet may say Amber ✔ — we go with math]
Q5: Amber ✘, Alfie ✔
Q6: Amber ✔, Alfie ✘
Q7: Amber ✔, Alfie ✘
Q8: Amber ✘, Alfie ✔
Q9: Amber ✔, Alfie ✘
Q10: Amber ✘, Alfie ✔

For Q4, since both are wrong, but the worksheet might expect Amber to be correct, I need to decide.

Wait — let me think differently. Maybe in Q4, the number line is only the point? But no, it has an arrow.

Another idea: perhaps the arrow is not part of the inequality? No, standard interpretation includes the arrow.

I recall that in some curricula, if there's a closed circle and an arrow, it's inclusive.

So I stand by: correct is x ≥ 0.

Thus, Amber’s x > 0 is missing the equality, so wrong.

Alfie’s x=0 is too narrow.

So both trash.

But to complete the task, I'll provide the accurate assessment.

Final Answer per question:

We need to output for each whether Amber and Alfie are tick or trash.

Since the user didn't specify how to format the final answer, but based on the task, likely we need to say for each question who is correct.

But the instruction says "Final Answer" — probably summarize.

Looking back at the user's request: "Solve the problem accurately." and the problem is to tick or trash Amber and Alfie's answers for each question.

So perhaps list for each question the evaluation.

But to keep it simple, since it's a worksheet, maybe state which ones are correct.

Alternatively, since the options are false, just give the final verdicts.

I think the best way is to list for each question whether Amber and Alfie are correct or not.

But for Final Answer, perhaps:

After checking all:

Amber is correct for: Q6, Q7, Q9
Alfie is correct for: Q1, Q2, Q3, Q5, Q8, Q10
Both wrong for Q4

But Q4 is problematic.

Perhaps in the context of the worksheet, for Q4, since Amber's answer is highlighted green, we should consider her correct? But that would be teaching incorrectly.

I think as an educational assistant, I must teach correctly.

So I'll go with math.

Final Answer:

For each question, here is whether Amber and Alfie are correct (Tick) or incorrect (Trash):

1) Amber: Trash, Alfie: Tick
2) Amber: Trash, Alfie: Tick
3) Amber: Trash, Alfie: Tick
4) Amber: Trash, Alfie: Trash [correct inequality is x ≥ 0]
5) Amber: Trash, Alfie: Tick
6) Amber: Tick, Alfie: Trash
7) Amber: Tick, Alfie: Trash
8) Amber: Trash, Alfie: Tick
9) Amber: Tick, Alfie: Trash
10) Amber: Trash, Alfie: Tick

Note: For question 4, neither answer is fully correct; the accurate inequality is x ≥ 0.

But since the problem might expect us to follow the worksheet's coloring, and in the image Amber's answer is green for Q4, perhaps there's a different interpretation.

Another thought: maybe in Q4, the number line is only the ray starting at 0, but Amber wrote x > 0, which is almost correct except for the endpoint. In some multiple-choice contexts, they might accept it, but strictly speaking, it's wrong.

I think for accuracy, I'll keep it as both wrong.

So the final answer is the list above.

To box it, perhaps write:

Amber is correct in questions 6, 7, 9.
Alfie is correct in questions 1, 2, 3, 5, 8, 10.
Question 4: both incorrect.

But let's confirm Q4 once more.

Upon second thought, in the user's image description, for Q4, the number line is: "closed circle at 0, arrow to the right" — so x ≥ 0.

Amber: x > 0 — this is incorrect because it does not include 0.

Alfie: x = 0 — incorrect because it doesn't include values greater than 0.

So yes, both wrong.

Perhaps the worksheet has a mistake, but we report accurately.

So for the Final Answer, I'll summarize the ticks and trashes.

Since the response format requires a Final Answer section, and it should be concise, I'll list the evaluations.

But to make it clear:

Final Answer:
- Q1: Amber - Trash, Alfie - Tick
- Q2: Amber - Trash, Alfie - Tick
- Q3: Amber - Trash, Alfie - Tick
- Q4: Amber - Trash, Alfie - Trash
- Q5: Amber - Trash, Alfie - Tick
- Q6: Amber - Tick, Alfie - Trash
- Q7: Amber - Tick, Alfie - Trash
- Q8: Amber - Trash, Alfie - Tick
- Q9: Amber - Tick, Alfie - Trash
- Q10: Amber - Trash, Alfie - Tick

This is the accurate assessment based on standard mathematical conventions for number lines and inequalities.