Comprehensive worksheet featuring 40 algebraic equations designed to help students practice isolating variables.

To solve the given algebraic equations, we need to isolate the variable on one side of the equation. Here are the solutions for each equation, along with explanations:

---

Equation 1: \( x + 5 = 9 \)

- Subtract 5 from both sides:
\[
x + 5 - 5 = 9 - 5
\]
\[
x = 4
\]

Equation 2: \( x + 7 = 15 \)

- Subtract 7 from both sides:
\[
x + 7 - 7 = 15 - 7
\]
\[
x = 8
\]

Equation 3: \( x + 1 = 8 \)

- Subtract 1 from both sides:
\[
x + 1 - 1 = 8 - 1
\]
\[
x = 7
\]

Equation 4: \( x + 11 = 21 \)

- Subtract 11 from both sides:
\[
x + 11 - 11 = 21 - 11
\]
\[
x = 10
\]

Equation 5: \( x + 6 = 4 \)

- Subtract 6 from both sides:
\[
x + 6 - 6 = 4 - 6
\]
\[
x = -2
\]

Equation 6: \( x + 4 = 4 \)

- Subtract 4 from both sides:
\[
x + 4 - 4 = 4 - 4
\]
\[
x = 0
\]

Equation 7: \( y + 20 = 32 \)

- Subtract 20 from both sides:
\[
y + 20 - 20 = 32 - 20
\]
\[
y = 12
\]

Equation 8: \( y + 12 = 30 \)

- Subtract 12 from both sides:
\[
y + 12 - 12 = 30 - 12
\]
\[
y = 18
\]

Equation 9: \( t + 8 = 101 \)

- Subtract 8 from both sides:
\[
t + 8 - 8 = 101 - 8
\]
\[
t = 93
\]

Equation 10: \( r + 0.5 = 9 \)

- Subtract 0.5 from both sides:
\[
r + 0.5 - 0.5 = 9 - 0.5
\]
\[
r = 8.5
\]

Equation 11: \( x - 1 = 10 \)

- Add 1 to both sides:
\[
x - 1 + 1 = 10 + 1
\]
\[
x = 11
\]

Equation 12: \( x - 5 = 2 \)

- Add 5 to both sides:
\[
x - 5 + 5 = 2 + 5
\]
\[
x = 7
\]

Equation 13: \( x - 8 = 20 \)

- Add 8 to both sides:
\[
x - 8 + 8 = 20 + 8
\]
\[
x = 28
\]

Equation 14: \( x - 9 = -3 \)

- Add 9 to both sides:
\[
x - 9 + 9 = -3 + 9
\]
\[
x = 6
\]

Equation 15: \( x - 3 = 21 \)

- Add 3 to both sides:
\[
x - 3 + 3 = 21 + 3
\]
\[
x = 24
\]

Equation 16: \( x - 7 = 4 \)

- Add 7 to both sides:
\[
x - 7 + 7 = 4 + 7
\]
\[
x = 11
\]

Equation 17: \( y - 10 = 34 \)

- Add 10 to both sides:
\[
y - 10 + 10 = 34 + 10
\]
\[
y = 44
\]

Equation 18: \( t - 52 = 11 \)

- Add 52 to both sides:
\[
t - 52 + 52 = 11 + 52
\]
\[
t = 63
\]

Equation 19: \( t - 3.5 = 9 \)

- Add 3.5 to both sides:
\[
t - 3.5 + 3.5 = 9 + 3.5
\]
\[
t = 12.5
\]

Equation 20: \( p - 21 = -4 \)

- Add 21 to both sides:
\[
p - 21 + 21 = -4 + 21
\]
\[
p = 17
\]

Equation 21: \( 2x = 12 \)

- Divide both sides by 2:
\[
\frac{2x}{2} = \frac{12}{2}
\]
\[
x = 6
\]

Equation 22: \( 5x = 15 \)

- Divide both sides by 5:
\[
\frac{5x}{5} = \frac{15}{5}
\]
\[
x = 3
\]

Equation 23: \( 3x = -6 \)

- Divide both sides by 3:
\[
\frac{3x}{3} = \frac{-6}{3}
\]
\[
x = -2
\]

Equation 24: \( 8x = 32 \)

- Divide both sides by 8:
\[
\frac{8x}{8} = \frac{32}{8}
\]
\[
x = 4
\]

Equation 25: \( 4x = 14 \)

- Divide both sides by 4:
\[
\frac{4x}{4} = \frac{14}{4}
\]
\[
x = 3.5
\]

Equation 26: \( 9x = -27 \)

- Divide both sides by 9:
\[
\frac{9x}{9} = \frac{-27}{9}
\]
\[
x = -3
\]

Equation 27: \( 6x = 31 \)

- Divide both sides by 6:
\[
\frac{6x}{6} = \frac{31}{6}
\]
\[
x = \frac{31}{6}
\]

Equation 28: \( 11x = 88 \)

- Divide both sides by 11:
\[
\frac{11x}{11} = \frac{88}{11}
\]
\[
x = 8
\]

Equation 29: \( 3y = 17 \)

- Divide both sides by 3:
\[
\frac{3y}{3} = \frac{17}{3}
\]
\[
y = \frac{17}{3}
\]

Equation 30: \( 3.5p = 10.5 \)

- Divide both sides by 3.5:
\[
\frac{3.5p}{3.5} = \frac{10.5}{3.5}
\]
\[
p = 3
\]

Equation 31: \( 2x + 1 = 13 \)

- Subtract 1 from both sides:
\[
2x + 1 - 1 = 13 - 1
\]
\[
2x = 12
\]
- Divide both sides by 2:
\[
\frac{2x}{2} = \frac{12}{2}
\]
\[
x = 6
\]

Equation 32: \( 5x - 2 = 23 \)

- Add 2 to both sides:
\[
5x - 2 + 2 = 23 + 2
\]
\[
5x = 25
\]
- Divide both sides by 5:
\[
\frac{5x}{5} = \frac{25}{5}
\]
\[
x = 5
\]

Equation 33: \( 8t + 3 = 43 \)

- Subtract 3 from both sides:
\[
8t + 3 - 3 = 43 - 3
\]
\[
8t = 40
\]
- Divide both sides by 8:
\[
\frac{8t}{8} = \frac{40}{8}
\]
\[
t = 5
\]

Equation 34: \( 4x + 10 = 42 \)

- Subtract 10 from both sides:
\[
4x + 10 - 10 = 42 - 10
\]
\[
4x = 32
\]
- Divide both sides by 4:
\[
\frac{4x}{4} = \frac{32}{4}
\]
\[
x = 8
\]

Equation 35: \( 7x - 2 = 65 \)

- Add 2 to both sides:
\[
7x - 2 + 2 = 65 + 2
\]
\[
7x = 67
\]
- Divide both sides by 7:
\[
\frac{7x}{7} = \frac{67}{7}
\]
\[
x = \frac{67}{7}
\]

Equation 36: \( 3y + 4 = -11 \)

- Subtract 4 from both sides:
\[
3y + 4 - 4 = -11 - 4
\]
\[
3y = -15
\]
- Divide both sides by 3:
\[
\frac{3y}{3} = \frac{-15}{3}
\]
\[
y = -5
\]

Equation 37: \( 6t + 7 = 28 \)

- Subtract 7 from both sides:
\[
6t + 7 - 7 = 28 - 7
\]
\[
6t = 21
\]
- Divide both sides by 6:
\[
\frac{6t}{6} = \frac{21}{6}
\]
\[
t = \frac{21}{6} = \frac{7}{2}
\]

Equation 38: \( 7x - 1 = 25 \)

- Add 1 to both sides:
\[
7x - 1 + 1 = 25 + 1
\]
\[
7x = 26
\]
- Divide both sides by 7:
\[
\frac{7x}{7} = \frac{26}{7}
\]
\[
x = \frac{26}{7}
\]

Equation 39: \( 3p - 4 = -2 \)

- Add 4 to both sides:
\[
3p - 4 + 4 = -2 + 4
\]
\[
3p = 2
\]
- Divide both sides by 3:
\[
\frac{3p}{3} = \frac{2}{3}
\]
\[
p = \frac{2}{3}
\]

Equation 40: \( 12q + 3 = 36 \)

- Subtract 3 from both sides:
\[
12q + 3 - 3 = 36 - 3
\]
\[
12q = 33
\]
- Divide both sides by 12:
\[
\frac{12q}{12} = \frac{33}{12}
\]
\[
q = \frac{33}{12} = \frac{11}{4}
\]

---

Final Answers:

\[
\boxed{
\begin{aligned}
&1. x = 4, \quad 2. x = 8, \quad 3. x = 7, \quad 4. x = 10, \quad 5. x = -2, \quad 6. x = 0, \\
&7. y = 12, \quad 8. y = 18, \quad 9. t = 93, \quad 10. r = 8.5, \quad 11. x = 11, \quad 12. x = 7, \\
&13. x = 28, \quad 14. x = 6, \quad 15. x = 24, \quad 16. x = 11, \quad 17. y = 44, \quad 18. t = 63, \\
&19. t = 12.5, \quad 20. p = 17, \quad 21. x = 6, \quad 22. x = 3, \quad 23. x = -2, \quad 24. x = 4, \\
&25. x = 3.5, \quad 26. x = -3, \quad 27. x = \frac{31}{6}, \quad 28. x = 8, \quad 29. y = \frac{17}{3}, \quad 30. p = 3, \\
&31. x = 6, \quad 32. x = 5, \quad 33. t = 5, \quad 34. x = 8, \quad 35. x = \frac{67}{7}, \quad 36. y = -5, \\
&37. t = \frac{7}{2}, \quad 38. x = \frac{26}{7}, \quad 39. p = \frac{2}{3}, \quad 40. q = \frac{11}{4}.
\end{aligned}
}
\]