Solving Linear Equations worksheet for Grade D students, featuring algebra problems with negative, fraction, and decimal answers.

Problem: Solving Linear Equations

The task is to solve the given linear equations. Let's solve each equation step by step.

---

#### Section A

1. Equation: \( 4x + 10 = 30 \)
- Subtract 10 from both sides:
\[
4x = 20
\]
- Divide by 4:
\[
x = 5
\]

2. Equation: \( 4x - 8 = 20 \)
- Add 8 to both sides:
\[
4x = 28
\]
- Divide by 4:
\[
x = 7
\]

3. Equation: \( 5 - 2x = 65 \)
- Subtract 5 from both sides:
\[
-2x = 60
\]
- Divide by -2:
\[
x = -30
\]

4. Equation: \( 9 + 4x = -15 \)
- Subtract 9 from both sides:
\[
4x = -24
\]
- Divide by 4:
\[
x = -6
\]

5. Equation: \( 14 - 6x = 2 \)
- Subtract 14 from both sides:
\[
-6x = -12
\]
- Divide by -6:
\[
x = 2
\]

6. Equation: \( 2x - 3 = -3 \)
- Add 3 to both sides:
\[
2x = 0
\]
- Divide by 2:
\[
x = 0
\]

7. Equation: \( 5 + 10x = -15 \)
- Subtract 5 from both sides:
\[
10x = -20
\]
- Divide by 10:
\[
x = -2
\]

8. Equation: \( 10 - 7 = x \)
- Simplify the left side:
\[
x = 3
\]

9. Equation: \( -3 - 16 = x \)
- Simplify the left side:
\[
x = -19
\]

10. Equation: \( -4 = 12 - 2x \)
- Subtract 12 from both sides:
\[
-16 = -2x
\]
- Divide by -2:
\[
x = 8
\]

11. Equation: \( 25 - 46 = 2x \)
- Simplify the left side:
\[
-21 = 2x
\]
- Divide by 2:
\[
x = -\frac{21}{2}
\]

12. Equation: \( 8 - 9 = 5x \)
- Simplify the left side:
\[
-1 = 5x
\]
- Divide by 5:
\[
x = -\frac{1}{5}
\]

---

#### Section B

13. Equation: \( \frac{x}{3} + 11 = 19 \)
- Subtract 11 from both sides:
\[
\frac{x}{3} = 8
\]
- Multiply by 3:
\[
x = 24
\]

14. Equation: \( \frac{x}{5} - 6 = -1 \)
- Add 6 to both sides:
\[
\frac{x}{5} = 5
\]
- Multiply by 5:
\[
x = 25
\]

15. Equation: \( \frac{x}{7} - 6 = -4 \)
- Add 6 to both sides:
\[
\frac{x}{7} = 2
\]
- Multiply by 7:
\[
x = 14
\]

16. Equation: \( \frac{x}{9} - 8 = -10 \)
- Add 8 to both sides:
\[
\frac{x}{9} = -2
\]
- Multiply by 9:
\[
x = -18
\]

17. Equation: \( \frac{x}{3} + 6 = -3 \)
- Subtract 6 from both sides:
\[
\frac{x}{3} = -9
\]
- Multiply by 3:
\[
x = -27
\]

18. Equation: \( \frac{x}{5} - 6 = -8 \)
- Add 6 to both sides:
\[
\frac{x}{5} = -2
\]
- Multiply by 5:
\[
x = -10
\]

19. Equation: \( \frac{x}{11} - 6 = -9 \)
- Add 6 to both sides:
\[
\frac{x}{11} = -3
\]
- Multiply by 11:
\[
x = -33
\]

20. Equation: \( \frac{x}{8} + 3 = -3 \)
- Subtract 3 from both sides:
\[
\frac{x}{8} = -6
\]
- Multiply by 8:
\[
x = -48
\]

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1) & x = 5 \\
2) & x = 7 \\
3) & x = -30 \\
4) & x = -6 \\
5) & x = 2 \\
6) & x = 0 \\
7) & x = -2 \\
8) & x = 3 \\
9) & x = -19 \\
10) & x = 8 \\
11) & x = -\frac{21}{2} \\
12) & x = -\frac{1}{5} \\
13) & x = 24 \\
14) & x = 25 \\
15) & x = 14 \\
16) & x = -18 \\
17) & x = -27 \\
18) & x = -10 \\
19) & x = -33 \\
20) & x = -48 \\
\end{array}
}
\]