Linear Equation Worksheets (printable, online, answers, examples) - Free Printable

To solve each of the given linear equations, we will follow a systematic approach: expand, simplify, isolate the variable, and solve for \( x \). Let's go through each equation step by step.

---

Equation 1: \( 5x + 2(2x - 4) = 55 \)

1. Expand the parentheses:
\[
5x + 2(2x - 4) = 55
\]
\[
5x + 4x - 8 = 55
\]

2. Combine like terms:
\[
9x - 8 = 55
\]

3. Isolate the term with \( x \):
\[
9x = 55 + 8
\]
\[
9x = 63
\]

4. Solve for \( x \):
\[
x = \frac{63}{9}
\]
\[
x = 7
\]

Solution: \( x = 7 \)

---

Equation 2: \( 7x + 4(x - 9) = 41 \)

1. Expand the parentheses:
\[
7x + 4(x - 9) = 41
\]
\[
7x + 4x - 36 = 41
\]

2. Combine like terms:
\[
11x - 36 = 41
\]

3. Isolate the term with \( x \):
\[
11x = 41 + 36
\]
\[
11x = 77
\]

4. Solve for \( x \):
\[
x = \frac{77}{11}
\]
\[
x = 7
\]

Solution: \( x = 7 \)

---

Equation 3: \( 3x + 2(x - 6) = 33 \)

1. Expand the parentheses:
\[
3x + 2(x - 6) = 33
\]
\[
3x + 2x - 12 = 33
\]

2. Combine like terms:
\[
5x - 12 = 33
\]

3. Isolate the term with \( x \):
\[
5x = 33 + 12
\]
\[
5x = 45
\]

4. Solve for \( x \):
\[
x = \frac{45}{5}
\]
\[
x = 9
\]

Solution: \( x = 9 \)

---

Equation 4: \( 4x + 3(3x + 7) = 86 \)

1. Expand the parentheses:
\[
4x + 3(3x + 7) = 86
\]
\[
4x + 9x + 21 = 86
\]

2. Combine like terms:
\[
13x + 21 = 86
\]

3. Isolate the term with \( x \):
\[
13x = 86 - 21
\]
\[
13x = 65
\]

4. Solve for \( x \):
\[
x = \frac{65}{13}
\]
\[
x = 5
\]

Solution: \( x = 5 \)

---

Equation 5: \( 2x + 5(4x - 7) = 75 \)

1. Expand the parentheses:
\[
2x + 5(4x - 7) = 75
\]
\[
2x + 20x - 35 = 75
\]

2. Combine like terms:
\[
22x - 35 = 75
\]

3. Isolate the term with \( x \):
\[
22x = 75 + 35
\]
\[
22x = 110
\]

4. Solve for \( x \):
\[
x = \frac{110}{22}
\]
\[
x = 5
\]

Solution: \( x = 5 \)

---

Equation 6: \( 97 = 7x + 2(x + 8) \)

1. Expand the parentheses:
\[
97 = 7x + 2(x + 8)
\]
\[
97 = 7x + 2x + 16
\]

2. Combine like terms:
\[
97 = 9x + 16
\]

3. Isolate the term with \( x \):
\[
97 - 16 = 9x
\]
\[
81 = 9x
\]

4. Solve for \( x \):
\[
x = \frac{81}{9}
\]
\[
x = 9
\]

Solution: \( x = 9 \)

---

Equation 7: \( 6x + 5(2x - 7) = 45 \)

1. Expand the parentheses:
\[
6x + 5(2x - 7) = 45
\]
\[
6x + 10x - 35 = 45
\]

2. Combine like terms:
\[
16x - 35 = 45
\]

3. Isolate the term with \( x \):
\[
16x = 45 + 35
\]
\[
16x = 80
\]

4. Solve for \( x \):
\[
x = \frac{80}{16}
\]
\[
x = 5
\]

Solution: \( x = 5 \)

---

Equation 8: \( 63 = 6x + 3(3x - 4) \)

1. Expand the parentheses:
\[
63 = 6x + 3(3x - 4)
\]
\[
63 = 6x + 9x - 12
\]

2. Combine like terms:
\[
63 = 15x - 12
\]

3. Isolate the term with \( x \):
\[
63 + 12 = 15x
\]
\[
75 = 15x
\]

4. Solve for \( x \):
\[
x = \frac{75}{15}
\]
\[
x = 5
\]

Solution: \( x = 5 \)

---

Equation 9: \( 3x + 4(x + 6) = 59 \)

1. Expand the parentheses:
\[
3x + 4(x + 6) = 59
\]
\[
3x + 4x + 24 = 59
\]

2. Combine like terms:
\[
7x + 24 = 59
\]

3. Isolate the term with \( x \):
\[
7x = 59 - 24
\]
\[
7x = 35
\]

4. Solve for \( x \):
\[
x = \frac{35}{7}
\]
\[
x = 5
\]

Solution: \( x = 5 \)

---

Equation 10: \( 82 = 2x + 2(3x + 5) \)

1. Expand the parentheses:
\[
82 = 2x + 2(3x + 5)
\]
\[
82 = 2x + 6x + 10
\]

2. Combine like terms:
\[
82 = 8x + 10
\]

3. Isolate the term with \( x \):
\[
82 - 10 = 8x
\]
\[
72 = 8x
\]

4. Solve for \( x \):
\[
x = \frac{72}{8}
\]
\[
x = 9
\]

Solution: \( x = 9 \)

---

Final Answers:

\[
\boxed{
\begin{aligned}
&x = 7, \quad x = 7, \quad x = 9, \quad x = 5, \quad x = 5, \\
&x = 9, \quad x = 5, \quad x = 5, \quad x = 5, \quad x = 9
\end{aligned}
}
\]