Linear Equations Worksheet for 8th - 9th Grade | Lesson Planet - Free Printable

Problem Description:

The task involves solving a series of simple linear equations for the variable \( x \). Each equation is in the form \( ax = b \), where \( a \) and \( b \) are constants, and we need to solve for \( x \).

Solution Approach:

To solve each equation \( ax = b \) for \( x \), we use the following steps:
1. Isolate the variable \( x \): Divide both sides of the equation by \( a \).
2. Simplify: Perform the division to find the value of \( x \).

Let's solve each equation step by step.

---

Equations and Solutions:

#### 1. \( 9x = 81 \)
\[
x = \frac{81}{9} = 9
\]
Solution: \( x = 9 \)

#### 2. \( 2x = 12 \)
\[
x = \frac{12}{2} = 6
\]
Solution: \( x = 6 \)

#### 3. \( 4x = 36 \)
\[
x = \frac{36}{4} = 9
\]
Solution: \( x = 9 \)

#### 4. \( 9x = 0 \)
\[
x = \frac{0}{9} = 0
\]
Solution: \( x = 0 \)

#### 5. \( 5x = 30 \)
\[
x = \frac{30}{5} = 6
\]
Solution: \( x = 6 \)

#### 6. \( 5x = 5 \)
\[
x = \frac{5}{5} = 1
\]
Solution: \( x = 1 \)

#### 7. \( 4x = 16 \)
\[
x = \frac{16}{4} = 4
\]
Solution: \( x = 4 \)

#### 8. \( 3x = 9 \)
\[
x = \frac{9}{3} = 3
\]
Solution: \( x = 3 \)

#### 9. \( 3x = 21 \)
\[
x = \frac{21}{3} = 7
\]
Solution: \( x = 7 \)

#### 10. \( 2x = 2 \)
\[
x = \frac{2}{2} = 1
\]
Solution: \( x = 1 \)

#### 11. \( 5x = 20 \)
\[
x = \frac{20}{5} = 4
\]
Solution: \( x = 4 \)

#### 12. \( 7x = 21 \)
\[
x = \frac{21}{7} = 3
\]
Solution: \( x = 3 \)

#### 13. \( 6x = 24 \)
\[
x = \frac{24}{6} = 4
\]
Solution: \( x = 4 \)

#### 14. \( 8x = 24 \)
\[
x = \frac{24}{8} = 3
\]
Solution: \( x = 3 \)

#### 15. \( 7x = 70 \)
\[
x = \frac{70}{7} = 10
\]
Solution: \( x = 10 \)

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Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & x = 9 \\
2. & x = 6 \\
3. & x = 9 \\
4. & x = 0 \\
5. & x = 6 \\
6. & x = 1 \\
7. & x = 4 \\
8. & x = 3 \\
9. & x = 7 \\
10. & x = 1 \\
11. & x = 4 \\
12. & x = 3 \\
13. & x = 4 \\
14. & x = 3 \\
15. & x = 10 \\
\end{array}
}
\]