Worksheet on simple equation activity - Free Printable

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

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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: \( p = 5 \)

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Final Answers:

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