This image shows the completed answer key for the Level 4 'Solving Linear Equations (A)' worksheet, with correct values for x highlighted in red.

Actually, you did not upload an image with a task — what you provided is the answer key for a worksheet titled “Solving Linear Equations (A)”, from Cazoom! educational resources.

This worksheet is designed to help students practice solving basic linear equations for the variable `x`. Since you’ve shared the *answers*, I’ll explain how to solve each type of equation found in the worksheet, using examples from each section. This will help you understand the methods behind the answers.

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## 📚 General Strategy for Solving Linear Equations

To solve for `x`, isolate it on one side of the equation by performing inverse operations:

- If something is added to `x`, subtract it from both sides.
- If something is subtracted from `x`, add it to both sides.
- If `x` is multiplied by a number, divide both sides by that number.
- If `x` is divided by a number, multiply both sides by that number.

Always do the same operation to both sides to keep the equation balanced.

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## 🔍 Section-by-Section Breakdown

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✔ Section A: Simple Addition/Subtraction

Equations like: `x + 3 = 11`

Example 1:
> x + 3 = 11
Subtract 3 from both sides:
→ x = 11 - 3
→ x = 8

Example 2:
> x - 5 = 7
Add 5 to both sides:
→ x = 7 + 5
→ x = 12

✔ These are solved by simple inverse operations.

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✔ Section B: Variable on Right or Mixed Operations

Equations like: `4 + x = 6` or `7 + x = 12`

Example 1:
> 4 + x = 6
Subtract 4 from both sides:
→ x = 6 - 4
→ x = 2

Example 2:
> 12 + x = 18
→ x = 18 - 12
→ x = 6

✔ Same as Section A — just rearranged.

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✔ Section C: Subtraction from x

Equations like: `x - 4 = 7`

Example 1:
> x - 4 = 7
Add 4 to both sides:
→ x = 7 + 4
→ x = 11

Example 2:
> x - 10 = 2
→ x = 2 + 10
→ x = 12

✔ Again, inverse operation: add the subtracted number.

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✔ Section D: Multiplication Equations

Equations like: `2x = 6`

Example 1:
> 2x = 6
Divide both sides by 2:
→ x = 6 ÷ 2
→ x = 3

Example 2:
> 5x = 15
→ x = 15 ÷ 5
→ x = 3

✔ Divide both sides by the coefficient of `x`.

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✔ Section E: Division Equations

Equations like: `x/3 = 4`

Example 1:
> x/3 = 4
Multiply both sides by 3:
→ x = 4 × 3
→ x = 12

Example 2:
> x/5 = 7
→ x = 7 × 5
→ x = 35

✔ Multiply both sides by the denominator.

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✔ Section F: Mixed and Slightly Harder Equations

Includes multi-step equations like: `4x = 48`, `x + 13 = 22`, `12x - 19 = 30`, etc.

Example 1 (Simple multiplication):
> 4x = 48
→ x = 48 ÷ 4
→ x = 12

Example 2 (Addition):
> x + 13 = 22
→ x = 22 - 13
→ x = 9

Example 3 (Two-step):
> 12x - 19 = 30
Step 1: Add 19 to both sides → 12x = 49
Step 2: Divide by 12 → x = 49/12? Wait — but answer says x = 49? That’s a typo!

Wait — let’s check the answer key:

> 7) 12x - 19 = 30 → 49

That’s incorrect mathematically.

Let’s solve correctly:
> 12x - 19 = 30
Add 19: 12x = 49
Divide by 12: x = 49/12 ≈ 4.083...

But the answer key says 49, which suggests the equation might have been meant to be:

> 12x - 19 = 569 → then 12x = 588 → x = 49

OR — more likely — the answer key has a typo. The correct solution to `12x - 19 = 30` is x = 49/12, not 49.

✔ So while most answers are correct, some may contain errors — always double-check!

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## 💡 Pro Tip: How to Verify Answers

Plug your answer back into the original equation:

Example: For `x + 3 = 11`, if you got x=8:
→ 8 + 3 = 11 → ✔️ Correct!

For `2x = 6`, if you got x=3:
→ 2×3 = 6 → ✔️ Correct!

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## 🧠 Summary of Methods

| Equation Type | Method |
|-----------------------|--------------------------------|
| x + a = b | Subtract `a` |
| x - a = b | Add `a` |
| ax = b | Divide by `a` |
| x/a = b | Multiply by `a` |
| ax + b = c | Subtract `b`, then divide by `a` |

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## ✔ Final Answer

You didn’t provide a specific problem to solve — you provided the answer sheet. But now you know how to solve every type of equation on this worksheet!

If you want to test yourself, pick any problem from the worksheet (without looking at the answer), solve it using the methods above, and verify your result.

If you’d like me to walk through a specific problem from the sheet, just tell me the section and number (e.g., “Section F, problem 7”) — and I’ll solve it step by step!

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📌 Note: There appears to be a mistake in the answer key for Section F, problem 7 (`12x - 19 = 30` → answer listed as 49). Correct solution is x = 49/12.

Let me know if you’d like corrections or explanations for specific problems!