Which of the following is not a linear equation

Options

A. `3x+3=5x+2`
B. `x^(2)+5=3x-5`
C. `7/3x-5=4x-3`
D. `(x+2)^(2)=x^(2)-8`

Answer

To determine which of the following equations is not a linear equation, we need to analyze each option based on the definition of a linear equation. A linear equation in two variables is generally of the form \( ax + by + c = 0 \) or can be simplified to this form, where the highest power of the variable is 1.

### Step-by-Step Solution:

1. **Identify the Options**: We need to evaluate each option provided to see if it is a linear equation.

2. **Evaluate the First Option**:
- The first option is \( 3x + 3 = 0 \).
- This can be rearranged to \( 3x = -3 \), which simplifies to \( x = -1 \).
- Since the highest power of \( x \) is 1, this is a linear equation.

3. **Evaluate the Second Option**:
- The second option is \( x^2 + 5 = 3x - 5 \).
- Rearranging gives \( x^2 - 3x + 10 = 0 \).
- Here, the highest power of \( x \) is 2, indicating that this is a quadratic equation, not a linear equation.

4. **Evaluate the Third Option**:
- The third option is \( \frac{7}{3}x - 5 = 4x - 3 \).
- Rearranging gives \( \frac{7}{3}x - 4x + 5 - 3 = 0 \).
- This simplifies to \( \frac{7 - 12}{3}x + 2 = 0 \), or \( -\frac{5}{3}x + 2 = 0 \).
- Since the highest power of \( x \) is 1, this is a linear equation.

5. **Evaluate the Fourth Option**:
- The fourth option is \( (x + 2)^2 = x^2 - 8 \).
- Expanding the left side gives \( x^2 + 4x + 4 = x^2 - 8 \).
- Rearranging gives \( 4x + 12 = 0 \), which simplifies to \( 4x = -12 \) or \( x = -3 \).
- Since the highest power of \( x \) is 1, this is also a linear equation.

6. **Conclusion**:
- The only option that is not a linear equation is the second option: \( x^2 + 5 = 3x - 5 \).

### Final Answer:
The option that is not a linear equation is **Option 2: \( x^2 + 5 = 3x - 5 \)**.