7th Grade Math Worksheet: Solving Equations

Problem: Solving Equations

The task is to solve each of the given equations for the variable. Let's solve them step by step.

---

#### Equation 1: \( x - 3 = 6 \)

1. Start with the equation:
\[
x - 3 = 6
\]

2. To isolate \( x \), add 3 to both sides of the equation:
\[
x - 3 + 3 = 6 + 3
\]

3. Simplify:
\[
x = 9
\]

Solution: \( x = 9 \)

---

#### Equation 2: \( x - 12 = 14 \)

1. Start with the equation:
\[
x - 12 = 14
\]

2. To isolate \( x \), add 12 to both sides of the equation:
\[
x - 12 + 12 = 14 + 12
\]

3. Simplify:
\[
x = 26
\]

Solution: \( x = 26 \)

---

#### Equation 3: \( n - 8 = 12 \)

1. Start with the equation:
\[
n - 8 = 12
\]

2. To isolate \( n \), add 8 to both sides of the equation:
\[
n - 8 + 8 = 12 + 8
\]

3. Simplify:
\[
n = 20
\]

Solution: \( n = 20 \)

---

#### Equation 4: \( a - 9 = 15 \)

1. Start with the equation:
\[
a - 9 = 15
\]

2. To isolate \( a \), add 9 to both sides of the equation:
\[
a - 9 + 9 = 15 + 9
\]

3. Simplify:
\[
a = 24
\]

Solution: \( a = 24 \)

---

#### Equation 5: \( n - 9 = 13 \)

1. Start with the equation:
\[
n - 9 = 13
\]

2. To isolate \( n \), add 9 to both sides of the equation:
\[
n - 9 + 9 = 13 + 9
\]

3. Simplify:
\[
n = 22
\]

Solution: \( n = 22 \)

---

#### Equation 6: \( b - 8 = 9 \)

1. Start with the equation:
\[
b - 8 = 9
\]

2. To isolate \( b \), add 8 to both sides of the equation:
\[
b - 8 + 8 = 9 + 8
\]

3. Simplify:
\[
b = 17
\]

Solution: \( b = 17 \)

---

#### Equation 7: \( x - 5 = 16 \)

1. Start with the equation:
\[
x - 5 = 16
\]

2. To isolate \( x \), add 5 to both sides of the equation:
\[
x - 5 + 5 = 16 + 5
\]

3. Simplify:
\[
x = 21
\]

Solution: \( x = 21 \)

---

#### Equation 8: \( n - 6 = 17 \)

1. Start with the equation:
\[
n - 6 = 17
\]

2. To isolate \( n \), add 6 to both sides of the equation:
\[
n - 6 + 6 = 17 + 6
\]

3. Simplify:
\[
n = 23
\]

Solution: \( n = 23 \)

---

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \ x = 9 \\
2. & \ x = 26 \\
3. & \ n = 20 \\
4. & \ a = 24 \\
5. & \ n = 22 \\
6. & \ b = 17 \\
7. & \ x = 21 \\
8. & \ n = 23
\end{aligned}
}
\]