Year 7 Maths Worksheets | Cazoom Maths Worksheets - Free Printable

Let’s solve each equation step by step. We’ll isolate the variable x on one side of the equation by doing the same thing to both sides (like subtracting or dividing).

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Section A

1) 7x + 9 = 23
→ Subtract 9 from both sides: 7x = 14
→ Divide by 7: x = 2

2) 5x + 7 = 42
→ Subtract 7: 5x = 35
→ Divide by 5: x = 7

3) 4x + 3 = 51
→ Subtract 3: 4x = 48
→ Divide by 4: x = 12

4) 9x + 5 = 41
→ Subtract 5: 9x = 36
→ Divide by 9: x = 4

5) 4x + 2 = 34
→ Subtract 2: 4x = 32
→ Divide by 4: x = 8

6) 11x + 3 = 36
→ Subtract 3: 11x = 33
→ Divide by 11: x = 3

7) 10x + 2 = 72
→ Subtract 2: 10x = 70
→ Divide by 10: x = 7

8) 7x + 3 = 52
→ Subtract 3: 7x = 49
→ Divide by 7: x = 7

9) 6x + 5 = 17
→ Subtract 5: 6x = 12
→ Divide by 6: x = 2

10) 4x + 7 = 9
→ Subtract 7: 4x = 2
→ Divide by 4: x = 0.5

11) 8x + 11 = 15
→ Subtract 11: 8x = 4
→ Divide by 8: x = 0.5

12) 4x + 17 = 18
→ Subtract 17: 4x = 1
→ Divide by 4: x = 0.25

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Section B

1) 1 + 6x = 19
→ Subtract 1: 6x = 18
→ Divide by 6: x = 3

2) 9 + 7x = 30
→ Subtract 9: 7x = 21
→ Divide by 7: x = 3

3) 3 + 2x = 17
→ Subtract 3: 2x = 14
→ Divide by 2: x = 7

4) 11 + 5x = 71
→ Subtract 11: 5x = 60
→ Divide by 5: x = 12

5) 5 + 3x = 32
→ Subtract 5: 3x = 27
→ Divide by 3: x = 9

6) 4 + 5x = 44
→ Subtract 4: 5x = 40
→ Divide by 5: x = 8

7) 23 = x + 8
→ Subtract 8: 15 = x → x = 15

8) 28 = 3x + 1
→ Subtract 1: 27 = 3x
→ Divide by 3: x = 9

9) 53 = 8x + 5
→ Subtract 5: 48 = 8x
→ Divide by 8: x = 6

10) 13 = 11 + 4x
→ Subtract 11: 2 = 4x
→ Divide by 4: x = 0.5

11) 7 = 8x + 3
→ Subtract 3: 4 = 8x
→ Divide by 8: x = 0.5

12) 12 = 7 + 15x
→ Subtract 7: 5 = 15x
→ Divide by 15: x = 1/3 ≈ 0.333... (but we'll keep it as fraction if needed — here, decimal is fine for this level)

Wait — let’s check that last one again:

12 = 7 + 15x
→ 12 - 7 = 15x → 5 = 15x → x = 5/15 = 1/3 → which is approximately 0.333, but since other answers are decimals or whole numbers, maybe write as fraction? But in context, probably acceptable as 1/3 or 0.33. However, looking at previous problems, they use decimals like 0.5 and 0.25, so 1/3 is okay — but let’s see if it simplifies nicely. Actually, 5 ÷ 15 = 1/3. So x = 1/3.

But wait — maybe I made a mistake? Let me double-check all Section B quickly.

Actually, no — calculations are correct. For #12, x = 1/3.

But let’s confirm with original: 7 + 15*(1/3) = 7 + 5 = 12 ✔️

So yes, x = 1/3.

However, in many school contexts, they might prefer decimal — but 1/3 is exact. Since others used 0.5, 0.25, etc., perhaps write as 0.33? But better to be precise.

Looking back at problem 10 and 11: they gave 0.5, which is exact. Here, 1/3 is not terminating. Maybe leave as fraction? But the worksheet doesn’t specify.

Actually, let’s check the original image — oh wait, I can’t describe image, but based on standard practice, if it divides evenly, use decimal; otherwise, fraction.

But 5/15 reduces to 1/3. So I’ll write x = 1/3.

Alternatively, maybe the problem expects decimal? Let’s see — in Section A, #10 and #11 gave 0.5, which is exact. #12 gave 0.25. So for consistency, perhaps write 1/3 as 0.33? But that’s approximate.

Actually, in math, unless specified, we should give exact value. So x = 1/3.

But let’s proceed — I think for this level, they may accept 1/3 or 0.33. To be safe, I’ll use fraction where necessary.

Wait — actually, rechecking: 12 = 7 + 15x → 5 = 15x → x = 5/15 = 1/3. Yes.

But let’s move on — I’ll note it.

Actually, upon second thought — in the answer key style, they might expect simplified fraction. So x = 1/3.

But let’s continue solving rest.

Section C coming up — similar steps.

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Section C

1) 4x – 1 = 31
→ Add 1: 4x = 32
→ Divide by 4: x = 8

2) 3x – 4 = 29
→ Add 4: 3x = 33
→ Divide by 3: x = 11

3) 6x – 5 = 31
→ Add 5: 6x = 36
→ Divide by 6: x = 6

4) 8x – 2 = 46
→ Add 2: 8x = 48
→ Divide by 8: x = 6

5) 2x – 7 = 21
→ Add 7: 2x = 28
→ Divide by 2: x = 14

6) 7x – 3 = 18
→ Add 3: 7x = 21
→ Divide by 7: x = 3

7) 9x – 4 = 32
→ Add 4: 9x = 36
→ Divide by 9: x = 4

8) 5x – 1 = 64
→ Add 1: 5x = 65
→ Divide by 5: x = 13

9) 12x – 9 = 39
→ Add 9: 12x = 48
→ Divide by 12: x = 4

10) 2x – 1 = 2
→ Add 1: 2x = 3
→ Divide by 2: x = 1.5

11) 4x – 8 = 10
→ Add 8: 4x = 18
→ Divide by 4: x = 4.5

12) 15x – 2 = 3
→ Add 2: 15x = 5
→ Divide by 15: x = 5/15 = 1/3 ≈ 0.333...

Again, x = 1/3.

Check: 15*(1/3) - 2 = 5 - 2 = 3 ✔️

So for Section B #12 and Section C #12, x = 1/3.

Now, compiling all answers.

I need to list them clearly.

Final Answer will be a list of all solutions in order.

Let me write them out section by section.

Section A:
1) 2
2) 7
3) 12
4) 4
5) 8
6) 3
7) 7
8) 7
9) 2
10) 0.5
11) 0.5
12) 0.25

Section B:
1) 3
2) 3
3) 7
4) 12
5) 9
6) 8
7) 15
8) 9
9) 6
10) 0.5
11) 0.5
12) 1/3 (or 0.333..., but I'll use fraction for accuracy)

Section C:
1) 8
2) 11
3) 6
4) 6
5) 14
6) 3
7) 4
8) 13
9) 4
10) 1.5
11) 4.5
12) 1/3

For consistency, since some are fractions, and others decimals, but in the worksheet, they have blanks, so probably expect numerical values.

In Section A #10 and #11, 0.5 is fine. #12 is 0.25.

For 1/3, it's repeating, so perhaps write as fraction.

But let me check if any other problems result in fractions — only these two.

To match the format, perhaps write all as decimals where possible, but 1/3 cannot be written exactly as decimal.

Since the instruction is to solve accurately, I should use exact values.

So for x = 1/3, I'll write it as \frac{1}{3} or just "1/3".

In the final answer, I can list them as numbers.

Perhaps the expected answer is decimal approximation, but I think for correctness, fraction is better.

Looking at the problem source — Cazoom Maths — they often accept fractions.

So I'll go with fractions for non-terminating decimals.

Thus:

Section B #12: x = 1/3

Section C #12: x = 1/3

Now, for the Final Answer, I need to provide all answers in order.

The user didn't specify how to present, but since it's a worksheet with numbered questions, I'll list them by section and number.

But the Final Answer should be concise — perhaps a list.

Since it's multiple parts, I'll write:

Final Answer:

Section A:
1) 2
2) 7
3) 12
4) 4
5) 8
6) 3
7) 7
8) 7
9) 2
10) 0.5
11) 0.5
12) 0.25

Section B:
1) 3
2) 3
3) 7
4) 12
5) 9
6) 8
7) 15
8) 9
9) 6
10) 0.5
11) 0.5
12) \frac{1}{3}

Section C:
1) 8
2) 11
3) 6
4) 6
5) 14
6) 3
7) 4
8) 13
9) 4
10) 1.5
11) 4.5
12) \frac{1}{3}

To make it neat, I can write without sections, but since the worksheet has sections, better to keep.

For the boxed answer, perhaps list all values in order.

But the instruction says "final correct answer", and since there are many, I need to present them clearly.

I think listing by section is fine.

Note: In Section B #7, it's 23 = x + 8, so x=15, which is correct.

All seem verified.

So, proceeding to Final Answer.