Jubal wrote the four equations below. He examined them, without solving them, to determine which equation has no solution.


Which of Jubal’s equations has no solution?

To determine which of Jubal’s equations has no solution, we would typically look for equations where the variable terms cancel out, leaving a statement that is clearly false (such as \(5 = 3\)).

However, since you didn't provide the specific equations, I can guide you on how to approach this problem generally:

### Steps to Determine if an Equation Has No Solution

1. **Simplify the Equation**: Combine like terms on both sides of the equation.

2. **Look for Contradictions**: After simplifying, if the variable terms cancel out and you are left with a statement like \( a = b \), where \( a \) and \( b \) are different numbers (e.g., \( 2 = 3 \)), then the equation has no solution.

3. **Check for Identical Terms**: If the simplified form of the equation results in something like \( a = a \) or \( 0 = 0 \), then the equation has infinitely many solutions.

### Example Process

Let's say the equations were:

1. \( 2x + 5 = 2x + 7 \)
2. \( 3x - 4 = 3x - 4 \)
3. \( x + 2 = x + 2 + 1 \)
4. \( 4x - 2 = 4x + 3 \)

#### Simplify Each Equation:

1. **\( 2x + 5 = 2x + 7 \)**
   - Subtract \( 2x \) from both sides: \( 5 = 7 \) (Contradiction, so no solution)

2. **\( 3x - 4 = 3x - 4 \)**
   - Subtract \( 3x \) from both sides: \( -4 = -4 \) (True statement, so infinitely many solutions)

3. **\( x + 2 = x + 3 \)**
   - Subtract \( x \) from both sides: \( 2 = 3 \) (Contradiction, so no solution)

4. **\( 4x - 2 = 4x + 3 \)**
   - Subtract \( 4x \) from both sides: \( -2 = 3 \) (Contradiction, so no solution)

In these examples, equations 1, 3, and 4 have no solutions.

### Conclusion:
To find out which of Jubal's equations has no solution, apply the steps above. Simplify each equation, and identify if any lead to a contradiction where the variable cancels out and leaves a false statement.

If you have the specific equations, I can help determine which one has no solution.

Would you like further details or have any other questions?

Here are some related questions you might consider:

1. How can you identify if an equation has infinitely many solutions?
2. What does it mean if an equation has a single solution?
3. How do you solve a system of equations to find the number of solutions?
4. What are the key indicators of a contradiction in an equation?
5. Can two different linear equations ever have the same solution?
6. How does the concept of no solutions apply to real-world problems?
7. What happens if an equation results in a statement like \( 0 = 0 \)?
8. How can you verify your work when solving an equation?

**Tip:** When examining equations, always simplify fully before making any conclusions about the number of solutions.

Explore how to identify equations with no solution through analysis and examples. Learn the steps to simplify equations, look for contradictions, and determine the presence of solutions. Suitable for students in 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