Which of the following is a linear equation in one variable?

Options

A. `(3x-1)^(2)= 9x^(2) + 4x- 4`
B. `(9x- 2)^(2)= 5x- 5x^(2) + 5`
C. `2x^(2)= 3x- 2`
D. None of these

Answer

To determine which of the given options is a linear equation in one variable, we need to follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of a Linear Equation:**
A linear equation in one variable is an equation of the form \( ax + b = 0 \), where \( a \) and \( b \) are constants, and the highest power of the variable \( x \) is 1.

2. **Identify the Given Equations:**
Let's assume we have three equations to analyze:
- Equation 1: \( 3x - 1 = 9x^2 + 4x - 4 \)
- Equation 2: \( (9x - 2)^2 = 5x - 5x^2 + 5 \)
- Equation 3: \( 2x^2 + 3x - 2 = 0 \)

3. **Analyze Each Equation:**
- **For Equation 1:**
- Rearranging gives us \( 3x - 1 - 9x^2 - 4x + 4 = 0 \).
- This simplifies to \( -9x^2 - x + 3 = 0 \).
- The highest power of \( x \) is 2, so this is **not a linear equation**.

- **For Equation 2:**
- Expanding \( (9x - 2)^2 \) gives \( 81x^2 - 36x + 4 \).
- Rearranging gives us \( 81x^2 - 36x + 4 - 5x + 5x^2 - 5 = 0 \).
- This simplifies to \( 86x^2 - 41x - 1 = 0 \).
- The highest power of \( x \) is 2, so this is **not a linear equation**.

- **For Equation 3:**
- Rearranging gives us \( 2x^2 + 3x - 2 = 0 \).
- The highest power of \( x \) is 2, so this is **not a linear equation**.

4. **Conclusion:**
After analyzing all three equations, we find that none of them are linear equations in one variable. Therefore, if we had to choose one from the options, we would conclude that **none of these options represent a linear equation in one variable**.