Seventh Grade Math Worksheets | 7th grade math worksheets, Algebra ... - Free Printable

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 for Equation 1:
\[
\boxed{x = 9}
\]

---

#### 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 for Equation 2:
\[
\boxed{x = 26}
\]

---

#### 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 for Equation 3:
\[
\boxed{n = 20}
\]

---

#### 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 for Equation 4:
\[
\boxed{a = 24}
\]

---

#### 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 for Equation 5:
\[
\boxed{n = 22}
\]

---

#### 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 for Equation 6:
\[
\boxed{b = 17}
\]

---

#### 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 for Equation 7:
\[
\boxed{x = 21}
\]

---

#### 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 for Equation 8:
\[
\boxed{n = 23}
\]

---

Final Answers:

1. \( x = 9 \)
2. \( x = 26 \)
3. \( n = 20 \)
4. \( a = 24 \)
5. \( n = 22 \)
6. \( b = 17 \)
7. \( x = 21 \)
8. \( n = 23 \)

\[
\boxed{x = 9, x = 26, n = 20, a = 24, n = 22, b = 17, x = 21, n = 23}
\]