Math worksheet for creating and solving equations based on word problems.

Problem Analysis:

The task involves creating equations based on given descriptions and solving for the variable \( x \). The first equation is already provided as an example: \( 3x + 5 = 14 \). We need to follow a similar approach for the remaining descriptions.

Step-by-Step Solution:

#### 1. Description: I subtract 5 from it. The answer is 8.
- Equation: If you subtract 5 from \( x \), the result is 8. This can be written as:
\[
x - 5 = 8
\]
- Solve for \( x \):
\[
x - 5 = 8 \implies x = 8 + 5 \implies x = 13
\]

#### 2. Description: I multiply it by 4 and subtract 4. The answer is 10.
- Equation: If you multiply \( x \) by 4 and then subtract 4, the result is 10. This can be written as:
\[
4x - 4 = 10
\]
- Solve for \( x \):
\[
4x - 4 = 10 \implies 4x = 10 + 4 \implies 4x = 14 \implies x = \frac{14}{4} \implies x = 3.5
\]

#### 3. Description: I divide it by 4. The answer is 8.
- Equation: If you divide \( x \) by 4, the result is 8. This can be written as:
\[
\frac{x}{4} = 8
\]
- Solve for \( x \):
\[
\frac{x}{4} = 8 \implies x = 8 \times 4 \implies x = 32
\]

#### 4. Description: I multiply it by 5. The answer is 10.
- Equation: If you multiply \( x \) by 5, the result is 10. This can be written as:
\[
5x = 10
\]
- Solve for \( x \):
\[
5x = 10 \implies x = \frac{10}{5} \implies x = 2
\]

#### 5. Description: I subtract 5 and divide by 2.
- Equation: If you subtract 5 from \( x \) and then divide the result by 2, the description is incomplete because it does not specify the final answer. Assuming the final answer is given as \( y \), the equation would be:
\[
\frac{x - 5}{2} = y
\]
- Since the problem does not provide a specific value for \( y \), we cannot solve for \( x \) without additional information. However, if we assume the final answer is a specific number (e.g., 3), the equation would be:
\[
\frac{x - 5}{2} = 3
\]
- Solve for \( x \):
\[
\frac{x - 5}{2} = 3 \implies x - 5 = 3 \times 2 \implies x - 5 = 6 \implies x = 6 + 5 \implies x = 11
\]

Final Answers:

\[
\begin{array}{|c|c|c|}
\hline
\text{I think of a number... } x & \text{Equation} & x = \\
\hline
\text{I multiply it by 3 and add 5. The answer is 14.} & 3x + 5 = 14 & 3 \\
\hline
\text{I subtract 5 from it. The answer is 8.} & x - 5 = 8 & 13 \\
\hline
\text{I multiply it by 4 and subtract 4. The answer is 10.} & 4x - 4 = 10 & 3.5 \\
\hline
\text{I divide it by 4. The answer is 8.} & \frac{x}{4} = 8 & 32 \\
\hline
\text{I multiply it by 5. The answer is 10.} & 5x = 10 & 2 \\
\hline
\text{I subtract 5 and divide by 2.} & \frac{x - 5}{2} = y & \text{(Depends on } y\text{)} \\
\hline
\end{array}
\]

If we assume the final answer for the last row is 3, then:
\[
\boxed{11}
\]