Math worksheet from Noble Guide Academy Abuja featuring ten algebraic equations to solve.

To solve the given equations, we will isolate the variables step by step. Let's go through each equation one by one.

---

Equation (1): \( 9c + 1 = 10 \)

1. Subtract 1 from both sides:
\[
9c + 1 - 1 = 10 - 1
\]
\[
9c = 9
\]

2. Divide both sides by 9:
\[
c = \frac{9}{9}
\]
\[
c = 1
\]

Solution: \( c = 1 \)

---

Equation (2): \( 6y - 5 = 7 \)

1. Add 5 to both sides:
\[
6y - 5 + 5 = 7 + 5
\]
\[
6y = 12
\]

2. Divide both sides by 6:
\[
y = \frac{12}{6}
\]
\[
y = 2
\]

Solution: \( y = 2 \)

---

Equation (3): \( 8 = 3a - 4 \)

1. Add 4 to both sides:
\[
8 + 4 = 3a - 4 + 4
\]
\[
12 = 3a
\]

2. Divide both sides by 3:
\[
a = \frac{12}{3}
\]
\[
a = 4
\]

Solution: \( a = 4 \)

---

Equation (4): \( \frac{m}{5} + 9 = 11 \)

1. Subtract 9 from both sides:
\[
\frac{m}{5} + 9 - 9 = 11 - 9
\]
\[
\frac{m}{5} = 2
\]

2. Multiply both sides by 5:
\[
m = 2 \times 5
\]
\[
m = 10
\]

Solution: \( m = 10 \)

---

Equation (5): \( 13 + 7x = 27 \)

1. Subtract 13 from both sides:
\[
13 + 7x - 13 = 27 - 13
\]
\[
7x = 14
\]

2. Divide both sides by 7:
\[
x = \frac{14}{7}
\]
\[
x = 2
\]

Solution: \( x = 2 \)

---

Equation (6): \( 17 - q = 6 \)

1. Subtract 17 from both sides:
\[
17 - q - 17 = 6 - 17
\]
\[
-q = -11
\]

2. Multiply both sides by -1:
\[
q = 11
\]

Solution: \( q = 11 \)

---

Equation (7): \( \frac{n - 31}{4} = 2 \)

1. Multiply both sides by 4:
\[
\frac{n - 31}{4} \times 4 = 2 \times 4
\]
\[
n - 31 = 8
\]

2. Add 31 to both sides:
\[
n - 31 + 31 = 8 + 31
\]
\[
n = 39
\]

Solution: \( n = 39 \)

---

Equation (8): \( 1 + 2r = 35 \)

1. Subtract 1 from both sides:
\[
1 + 2r - 1 = 35 - 1
\]
\[
2r = 34
\]

2. Divide both sides by 2:
\[
r = \frac{34}{2}
\]
\[
r = 17
\]

Solution: \( r = 17 \)

---

Equation (9): \( 42 + 5t = 8t \)

1. Subtract \( 5t \) from both sides:
\[
42 + 5t - 5t = 8t - 5t
\]
\[
42 = 3t
\]

2. Divide both sides by 3:
\[
t = \frac{42}{3}
\]
\[
t = 14
\]

Solution: \( t = 14 \)

---

Equation (10): \( 4p - 3 = 17 \)

1. Add 3 to both sides:
\[
4p - 3 + 3 = 17 + 3
\]
\[
4p = 20
\]

2. Divide both sides by 4:
\[
p = \frac{20}{4}
\]
\[
p = 5
\]

Solution: \( p = 5 \)

---

Final Answers:

\[
\boxed{
\begin{aligned}
&c = 1, \quad y = 2, \quad a = 4, \quad m = 10, \quad x = 2, \\
&q = 11, \quad n = 39, \quad r = 17, \quad t = 14, \quad p = 5
\end{aligned}
}
\]