7th Grade Math Worksheets - Free Printable

To solve the linear equations in the worksheet, we will isolate the variable \( x \) on one side of the equation. Let's go through each section step by step.

---

Section A

#### 1) \( 7x + 9 = 23 \)
\[
\begin{aligned}
7x + 9 &= 23 \\
7x &= 23 - 9 \\
7x &= 14 \\
x &= \frac{14}{7} \\
x &= 2
\end{aligned}
\]
Answer: \( x = 2 \)

#### 2) \( 5x + 7 = 42 \)
\[
\begin{aligned}
5x + 7 &= 42 \\
5x &= 42 - 7 \\
5x &= 35 \\
x &= \frac{35}{5} \\
x &= 7
\end{aligned}
\]
Answer: \( x = 7 \)

#### 3) \( 4x + 3 = 51 \)
\[
\begin{aligned}
4x + 3 &= 51 \\
4x &= 51 - 3 \\
4x &= 48 \\
x &= \frac{48}{4} \\
x &= 12
\end{aligned}
\]
Answer: \( x = 12 \)

#### 4) \( 9x + 5 = 41 \)
\[
\begin{aligned}
9x + 5 &= 41 \\
9x &= 41 - 5 \\
9x &= 36 \\
x &= \frac{36}{9} \\
x &= 4
\end{aligned}
\]
Answer: \( x = 4 \)

#### 5) \( 4x + 2 = 34 \)
\[
\begin{aligned}
4x + 2 &= 34 \\
4x &= 34 - 2 \\
4x &= 32 \\
x &= \frac{32}{4} \\
x &= 8
\end{aligned}
\]
Answer: \( x = 8 \)

#### 6) \( 11x + 3 = 36 \)
\[
\begin{aligned}
11x + 3 &= 36 \\
11x &= 36 - 3 \\
11x &= 33 \\
x &= \frac{33}{11} \\
x &= 3
\end{aligned}
\]
Answer: \( x = 3 \)

#### 7) \( 10x + 2 = 72 \)
\[
\begin{aligned}
10x + 2 &= 72 \\
10x &= 72 - 2 \\
10x &= 70 \\
x &= \frac{70}{10} \\
x &= 7
\end{aligned}
\]
Answer: \( x = 7 \)

#### 8) \( 7x + 3 = 52 \)
\[
\begin{aligned}
7x + 3 &= 52 \\
7x &= 52 - 3 \\
7x &= 49 \\
x &= \frac{49}{7} \\
x &= 7
\end{aligned}
\]
Answer: \( x = 7 \)

#### 9) \( 6x + 5 = 17 \)
\[
\begin{aligned}
6x + 5 &= 17 \\
6x &= 17 - 5 \\
6x &= 12 \\
x &= \frac{12}{6} \\
x &= 2
\end{aligned}
\]
Answer: \( x = 2 \)

#### 10) \( 4x + 7 = 9 \)
\[
\begin{aligned}
4x + 7 &= 9 \\
4x &= 9 - 7 \\
4x &= 2 \\
x &= \frac{2}{4} \\
x &= \frac{1}{2}
\end{aligned}
\]
Answer: \( x = \frac{1}{2} \)

#### 11) \( 8x + 11 = 15 \)
\[
\begin{aligned}
8x + 11 &= 15 \\
8x &= 15 - 11 \\
8x &= 4 \\
x &= \frac{4}{8} \\
x &= \frac{1}{2}
\end{aligned}
\]
Answer: \( x = \frac{1}{2} \)

#### 12) \( 4x + 17 = 18 \)
\[
\begin{aligned}
4x + 17 &= 18 \\
4x &= 18 - 17 \\
4x &= 1 \\
x &= \frac{1}{4}
\end{aligned}
\]
Answer: \( x = \frac{1}{4} \)

---

Section B

#### 1) \( 1 + 6x = 19 \)
\[
\begin{aligned}
1 + 6x &= 19 \\
6x &= 19 - 1 \\
6x &= 18 \\
x &= \frac{18}{6} \\
x &= 3
\end{aligned}
\]
Answer: \( x = 3 \)

#### 2) \( 9 + 7x = 30 \)
\[
\begin{aligned}
9 + 7x &= 30 \\
7x &= 30 - 9 \\
7x &= 21 \\
x &= \frac{21}{7} \\
x &= 3
\end{aligned}
\]
Answer: \( x = 3 \)

#### 3) \( 3 + 2x = 17 \)
\[
\begin{aligned}
3 + 2x &= 17 \\
2x &= 17 - 3 \\
2x &= 14 \\
x &= \frac{14}{2} \\
x &= 7
\end{aligned}
\]
Answer: \( x = 7 \)

#### 4) \( 11 + 5x = 71 \)
\[
\begin{aligned}
11 + 5x &= 71 \\
5x &= 71 - 11 \\
5x &= 60 \\
x &= \frac{60}{5} \\
x &= 12
\end{aligned}
\]
Answer: \( x = 12 \)

#### 5) \( 5 + 3x = 32 \)
\[
\begin{aligned}
5 + 3x &= 32 \\
3x &= 32 - 5 \\
3x &= 27 \\
x &= \frac{27}{3} \\
x &= 9
\end{aligned}
\]
Answer: \( x = 9 \)

#### 6) \( 4 + 5x = 44 \)
\[
\begin{aligned}
4 + 5x &= 44 \\
5x &= 44 - 4 \\
5x &= 40 \\
x &= \frac{40}{5} \\
x &= 8
\end{aligned}
\]
Answer: \( x = 8 \)

#### 7) \( 23 = x + 8 \)
\[
\begin{aligned}
23 &= x + 8 \\
x &= 23 - 8 \\
x &= 15
\end{aligned}
\]
Answer: \( x = 15 \)

#### 8) \( 28 = 3x + 1 \)
\[
\begin{aligned}
28 &= 3x + 1 \\
28 - 1 &= 3x \\
27 &= 3x \\
x &= \frac{27}{3} \\
x &= 9
\end{aligned}
\]
Answer: \( x = 9 \)

#### 9) \( 53 = 8x + 5 \)
\[
\begin{aligned}
53 &= 8x + 5 \\
53 - 5 &= 8x \\
48 &= 8x \\
x &= \frac{48}{8} \\
x &= 6
\end{aligned}
\]
Answer: \( x = 6 \)

#### 10) \( 13 = 11 + 4x \)
\[
\begin{aligned}
13 &= 11 + 4x \\
13 - 11 &= 4x \\
2 &= 4x \\
x &= \frac{2}{4} \\
x &= \frac{1}{2}
\end{aligned}
\]
Answer: \( x = \frac{1}{2} \)

#### 11) \( 7 = 8x + 3 \)
\[
\begin{aligned}
7 &= 8x + 3 \\
7 - 3 &= 8x \\
4 &= 8x \\
x &= \frac{4}{8} \\
x &= \frac{1}{2}
\end{aligned}
\]
Answer: \( x = \frac{1}{2} \)

#### 12) \( 12 = 7 + 15x \)
\[
\begin{aligned}
12 &= 7 + 15x \\
12 - 7 &= 15x \\
5 &= 15x \\
x &= \frac{5}{15} \\
x &= \frac{1}{3}
\end{aligned}
\]
Answer: \( x = \frac{1}{3} \)

---

Section C

#### 1) \( 4x - 1 = 31 \)
\[
\begin{aligned}
4x - 1 &= 31 \\
4x &= 31 + 1 \\
4x &= 32 \\
x &= \frac{32}{4} \\
x &= 8
\end{aligned}
\]
Answer: \( x = 8 \)

#### 2) \( 3x - 4 = 29 \)
\[
\begin{aligned}
3x - 4 &= 29 \\
3x &= 29 + 4 \\
3x &= 33 \\
x &= \frac{33}{3} \\
x &= 11
\end{aligned}
\]
Answer: \( x = 11 \)

#### 3) \( 6x - 5 = 31 \)
\[
\begin{aligned}
6x - 5 &= 31 \\
6x &= 31 + 5 \\
6x &= 36 \\
x &= \frac{36}{6} \\
x &= 6
\end{aligned}
\]
Answer: \( x = 6 \)

#### 4) \( 8x - 2 = 46 \)
\[
\begin{aligned}
8x - 2 &= 46 \\
8x &= 46 + 2 \\
8x &= 48 \\
x &= \frac{48}{8} \\
x &= 6
\end{aligned}
\]
Answer: \( x = 6 \)

#### 5) \( 2x - 7 = 21 \)
\[
\begin{aligned}
2x - 7 &= 21 \\
2x &= 21 + 7 \\
2x &= 28 \\
x &= \frac{28}{2} \\
x &= 14
\end{aligned}
\]
Answer: \( x = 14 \)

#### 6) \( 7x - 3 = 18 \)
\[
\begin{aligned}
7x - 3 &= 18 \\
7x &= 18 + 3 \\
7x &= 21 \\
x &= \frac{21}{7} \\
x &= 3
\end{aligned}
\]
Answer: \( x = 3 \)

#### 7) \( 9x - 4 = 32 \)
\[
\begin{aligned}
9x - 4 &= 32 \\
9x &= 32 + 4 \\
9x &= 36 \\
x &= \frac{36}{9} \\
x &= 4
\end{aligned}
\]
Answer: \( x = 4 \)

#### 8) \( 5x - 1 = 64 \)
\[
\begin{aligned}
5x - 1 &= 64 \\
5x &= 64 + 1 \\
5x &= 65 \\
x &= \frac{65}{5} \\
x &= 13
\end{aligned}
\]
Answer: \( x = 13 \)

#### 9) \( 12x - 9 = 39 \)
\[
\begin{aligned}
12x - 9 &= 39 \\
12x &= 39 + 9 \\
12x &= 48 \\
x &= \frac{48}{12} \\
x &= 4
\end{aligned}
\]
Answer: \( x = 4 \)

#### 10) \( 2x - 1 = 2 \)
\[
\begin{aligned}
2x - 1 &= 2 \\
2x &= 2 + 1 \\
2x &= 3 \\
x &= \frac{3}{2}
\end{aligned}
\]
Answer: \( x = \frac{3}{2} \)

#### 11) \( 4x - 8 = 10 \)
\[
\begin{aligned}
4x - 8 &= 10 \\
4x &= 10 + 8 \\
4x &= 18 \\
x &= \frac{18}{4} \\
x &= \frac{9}{2}
\end{aligned}
\]
Answer: \( x = \frac{9}{2} \)

#### 12) \( 15x - 2 = 3 \)
\[
\begin{aligned}
15x - 2 &= 3 \\
15x &= 3 + 2 \\
15x &= 5 \\
x &= \frac{5}{15} \\
x &= \frac{1}{3}
\end{aligned}
\]
Answer: \( x = \frac{1}{3} \)

---

Final Answers

\[
\boxed{
\begin{array}{lll}
\text{Section A:} & 2, 7, 12, 4, 8, 3, 7, 7, 2, \frac{1}{2}, \frac{1}{2}, \frac{1}{4} \\
\text{Section B:} & 3, 3, 7, 12, 9, 8, 15, 9, 6, \frac{1}{2}, \frac{1}{2}, \frac{1}{3} \\
\text{Section C:} & 8, 11, 6, 6, 14, 3, 4, 13, 4, \frac{3}{2}, \frac{9}{2}, \frac{1}{3}
\end{array}
}
\]