make a  two-column algebraic proof solving your equation Find an equation that can be solved in different ways.

To demonstrate a two-column algebraic proof, let's first create an equation that can be solved using different methods. We'll use the equation:

**Equation:**

\[ 2x + 3 = 11 \]

### Two-Column Proof (Method 1: Subtract and Divide)

| **Steps**          | **Reason**                          |
|--------------------|-------------------------------------|
| \( 2x + 3 = 11 \)  | Given equation                      |
| \( 2x + 3 - 3 = 11 - 3 \) | Subtract 3 from both sides      |
| \( 2x = 8 \)       | Simplify                            |
| \( \frac{2x}{2} = \frac{8}{2} \) | Divide both sides by 2          |
| \( x = 4 \)        | Simplify                            |

### Two-Column Proof (Method 2: Divide and Subtract)

| **Steps**          | **Reason**                          |
|--------------------|-------------------------------------|
| \( 2x + 3 = 11 \)  | Given equation                      |
| \( \frac{2x + 3}{2} = \frac{11}{2} \) | Divide both sides by 2        |
| \( x + \frac{3}{2} = \frac{11}{2} \) | Simplify                            |
| \( x + \frac{3}{2} - \frac{3}{2} = \frac{11}{2} - \frac{3}{2} \) | Subtract \(\frac{3}{2}\) from both sides |
| \( x = \frac{8}{2} \)  | Simplify                            |
| \( x = 4 \)        | Simplify                            |

### Conclusion

Both methods result in the same solution, \( x = 4 \), demonstrating that the equation \( 2x + 3 = 11 \) can be solved using different approaches, but still arrives at the same answer.

Would you like more details or have any questions? Here are some related questions to explore further:

1. How do you solve equations with variables on both sides?
2. What are the properties of equality used in solving equations?
3. How do you solve equations involving fractions?
4. How do you check if a solution to an equation is correct?
5. What are other methods to solve equations, such as factoring?

**Tip:** Always check your solution by substituting it back into the original equation to verify its correctness.

Explore a two-column algebraic proof solving an equation in multiple ways. Learn step-by-step how to solve the equation 2x + 3 = 11 using different methods, ensuring a clear understanding of algebraic concepts and problem-solving techniques. Suitable for Grades 7-9.

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