Simple equations worksheet - Free Printable

Let's solve each problem step by step.

---

Problem 1: The solution of \( 7n + 5 = 12 \)

#### Solution:
1. Start with the equation:
\[
7n + 5 = 12
\]

2. Subtract 5 from both sides to isolate the term with \( n \):
\[
7n = 12 - 5
\]
\[
7n = 7
\]

3. Divide both sides by 7 to solve for \( n \):
\[
n = \frac{7}{7}
\]
\[
n = 1
\]

#### Answer:
\[
\boxed{c)
}

---

Problem 2: The solution of the equation \( \frac{m}{3} = 3 \)

#### Solution:
1. Start with the equation:
\[
\frac{m}{3} = 3
\]

2. Multiply both sides by 3 to eliminate the denominator:
\[
m = 3 \times 3
\]
\[
m = 9
\]

#### Answer:
\[
\boxed{c)
}

---

Problem 3: The solution of \( 3(x - 1) + 8 = 11 \)

#### Solution:
1. Start with the equation:
\[
3(x - 1) + 8 = 11
\]

2. Subtract 8 from both sides to isolate the term with \( x \):
\[
3(x - 1) = 11 - 8
\]
\[
3(x - 1) = 3
\]

3. Divide both sides by 3:
\[
x - 1 = \frac{3}{3}
\]
\[
x - 1 = 1
\]

4. Add 1 to both sides to solve for \( x \):
\[
x = 1 + 1
\]
\[
x = 2
\]

#### Answer:
\[
\boxed{a)
}

---

Problem 4: Which of the following equations can be constructed with \( x = 2 \)

#### Solution:
We need to check which equation is satisfied when \( x = 2 \).

1. Option (a): \( x + 4 = 8 \)
\[
x + 4 = 8
\]
Substitute \( x = 2 \):
\[
2 + 4 = 6 \quad (\text{not } 8)
\]
This is not correct.

2. Option (b): \( 3x - 1 = 2 \)
\[
3x - 1 = 2
\]
Substitute \( x = 2 \):
\[
3(2) - 1 = 6 - 1 = 5 \quad (\text{not } 2)
\]
This is not correct.

3. Option (c): \( x - 2 = 2 \)
\[
x - 2 = 2
\]
Substitute \( x = 2 \):
\[
2 - 2 = 0 \quad (\text{not } 2)
\]
This is not correct.

4. Option (d): \( x + 5 = 7 \)
\[
x + 5 = 7
\]
Substitute \( x = 2 \):
\[
2 + 5 = 7 \quad (\text{correct})
\]
This is correct.

#### Answer:
\[
\boxed{d)
}

---

Problem 5: The solution of the equation \( 10 - 3y = 1 \)

#### Solution:
1. Start with the equation:
\[
10 - 3y = 1
\]

2. Subtract 10 from both sides to isolate the term with \( y \):
\[
-3y = 1 - 10
\]
\[
-3y = -9
\]

3. Divide both sides by -3 to solve for \( y \):
\[
y = \frac{-9}{-3}
\]
\[
y = 3
\]

#### Answer:
\[
\boxed{d)
}

---

Final Answers:

1. \( \boxed{c} \)
2. \( \boxed{c} \)
3. \( \boxed{a} \)
4. \( \boxed{d} \)
5. \( \boxed{d} \)