Let's solve the equation \(2x - 3 = 2x + 1\).

### Step 1: Subtract \(2x\) from both sides of the equation to eliminate the \(x\) terms.

\[
2x - 3 - 2x = 2x + 1 - 2x
\]

This simplifies to:

\[
-3 = 1
\]

### Step 2: Analyze the result

The equation \(-3 = 1\) is a contradiction, meaning it is not true. This indicates that the original equation has no solution.

### Conclusion

The equation \(2x - 3 = 2x + 1\) has no solution because it leads to a contradiction. This is known as an inconsistent equation.

Would you like more details or have any other questions?

---

Here are some related questions you might find interesting:

1. What is the difference between consistent, inconsistent, and dependent equations?
2. How can you identify when an equation has no solution without fully solving it?
3. What does it mean if the equation simplifies to something like \(0 = 0\)?
4. How would you handle a system of equations if one of them has no solution?
5. How does the graph of the equation \(2x - 3 = 2x + 1\) look, and what does it tell you about the solutions?

**Tip:** When both sides of an equation simplify to the same linear expression with different constants, the equation will have no solution.

Learn how to solve the equation 2x - 3 = 2x + 1 with a detailed explanation of why it leads to a contradiction. This problem explores algebraic concepts like linear equations and contradictions, suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation