This worksheet provides structured practice for students learning to solve basic linear equations by isolating the variable x.

Problem: Solving Linear Equations

The task is to solve the given linear equations to find the value of \( x \). Let's solve each section step by step.

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#### Section A: Solving Equations of the Form \( x + a = b \)

These equations involve adding a constant to \( x \). To solve for \( x \), we subtract the constant from both sides of the equation.

1. \( x + 3 = 11 \)
\[
x = 11 - 3 = 8
\]
Answer: \( x = 8 \)

2. \( x + 2 = 8 \)
\[
x = 8 - 2 = 6
\]
Answer: \( x = 6 \)

3. \( x + 5 = 7 \)
\[
x = 7 - 5 = 2
\]
Answer: \( x = 2 \)

4. \( x + 7 = 13 \)
\[
x = 13 - 7 = 6
\]
Answer: \( x = 6 \)

5. \( x + 4 = 14 \)
\[
x = 14 - 4 = 10
\]
Answer: \( x = 10 \)

6. \( x + 7 = 9 \)
\[
x = 9 - 7 = 2
\]
Answer: \( x = 2 \)

7. \( x + 3 = 9 \)
\[
x = 9 - 3 = 6
\]
Answer: \( x = 6 \)

8. \( x + 12 = 17 \)
\[
x = 17 - 12 = 5
\]
Answer: \( x = 5 \)

9. \( x + 6 = 24 \)
\[
x = 24 - 6 = 18
\]
Answer: \( x = 18 \)

10. \( x + 5 = 36 \)
\[
x = 36 - 5 = 31
\]
Answer: \( x = 31 \)

11. \( x + 8 = 43 \)
\[
x = 43 - 8 = 35
\]
Answer: \( x = 35 \)

12. \( x + 9 = 61 \)
\[
x = 61 - 9 = 52
\]
Answer: \( x = 52 \)

---

#### Section B: Solving Equations of the Form \( a + x = b \)

These equations are similar to Section A, where the constant is added to \( x \). We solve by subtracting the constant from both sides.

1. \( 4 + x = 6 \)
\[
x = 6 - 4 = 2
\]
Answer: \( x = 2 \)

2. \( 2 + x = 7 \)
\[
x = 7 - 2 = 5
\]
Answer: \( x = 5 \)

3. \( 8 + x = 11 \)
\[
x = 11 - 8 = 3
\]
Answer: \( x = 3 \)

4. \( 5 + x = 9 \)
\[
x = 9 - 5 = 4
\]
Answer: \( x = 4 \)

5. \( 7 + x = 12 \)
\[
x = 12 - 7 = 5
\]
Answer: \( x = 5 \)

6. \( 12 + x = 18 \)
\[
x = 18 - 12 = 6
\]
Answer: \( x = 6 \)

7. \( 14 + x = 23 \)
\[
x = 23 - 14 = 9
\]
Answer: \( x = 9 \)

8. \( 19 + x = 32 \)
\[
x = 32 - 19 = 13
\]
Answer: \( x = 13 \)

9. \( 7 + x = 40 \)
\[
x = 40 - 7 = 33
\]
Answer: \( x = 33 \)

10. \( 8 + x = 72 \)
\[
x = 72 - 8 = 64
\]
Answer: \( x = 64 \)

11. \( 11 + x = 64 \)
\[
x = 64 - 11 = 53
\]
Answer: \( x = 53 \)

12. \( 28 + x = 90 \)
\[
x = 90 - 28 = 62
\]
Answer: \( x = 62 \)

---

#### Section C: Solving Equations of the Form \( x - a = b \)

These equations involve subtracting a constant from \( x \). To solve for \( x \), we add the constant to both sides of the equation.

1. \( x - 4 = 7 \)
\[
x = 7 + 4 = 11
\]
Answer: \( x = 11 \)

2. \( x - 6 = 4 \)
\[
x = 4 + 6 = 10
\]
Answer: \( x = 10 \)

3. \( x - 1 = 6 \)
\[
x = 6 + 1 = 7
\]
Answer: \( x = 7 \)

4. \( x - 7 = 13 \)
\[
x = 13 + 7 = 20
\]
Answer: \( x = 20 \)

5. \( x - 10 = 2 \)
\[
x = 2 + 10 = 12
\]
Answer: \( x = 12 \)

6. \( x - 7 = 18 \)
\[
x = 18 + 7 = 25
\]
Answer: \( x = 25 \)

7. \( x - 11 = 8 \)
\[
x = 8 + 11 = 19
\]
Answer: \( x = 19 \)

8. \( x - 5 = 16 \)
\[
x = 16 + 5 = 21
\]
Answer: \( x = 21 \)

9. \( x - 9 = 25 \)
\[
x = 25 + 9 = 34
\]
Answer: \( x = 34 \)

10. \( x - 12 = 31 \)
\[
x = 31 + 12 = 43
\]
Answer: \( x = 43 \)

11. \( x - 16 = 29 \)
\[
x = 29 + 16 = 45
\]
Answer: \( x = 45 \)

12. \( x - 28 = 78 \)
\[
x = 78 + 28 = 106
\]
Answer: \( x = 106 \)

---

Final Answers:

- Section A:
\[
\boxed{8, 6, 2, 6, 10, 2, 6, 5, 18, 31, 35, 52}
\]

- Section B:
\[
\boxed{2, 5, 3, 4, 5, 6, 9, 13, 33, 64, 53, 62}
\]

- Section C:
\[
\boxed{11, 10, 7, 20, 12, 25, 19, 21, 34, 43, 45, 106}
\]