Question

Which of the following equations has no solutions? (1 point) - 6x + 4 = 6x + 3; 6x + 3 = - 6x + 3; 6x + 4 = 6x + 4 O - 6x + 4 = - 6x + 3

Answer 1

So which one

Answer 2

My answer choices are
- 6x + 4 = 6x + 3
6x + 3 = - 6x + 3
6 + 4 = 6x + 4
- 6x + 4 = - 6x + 3

Answer 3

To determine which of the given equations has no solutions, let's analyze each one:

1. **Equation:** \( 6x + 4 = 6x + 3 \)
- Subtract \( 6x \) from both sides:
- \( 4 = 3 \) (This is false, hence no solutions.)

2. **Equation:** \( 6x + 3 = -6x + 3 \)
- Add \( 6x \) to both sides:
- \( 12x + 3 = 3 \)
- Subtract 3 from both sides:
- \( 12x = 0 \) ⇒ \( x = 0 \) (This has a solution.)

3. **Equation:** \( 6x + 4 = 6x + 4 \)
- Subtract \( 6x + 4 \) from both sides:
- \( 0 = 0 \) (This is always true, hence infinitely many solutions.)

4. **Equation:** \( -6x + 4 = -6x + 3 \)
- Add \( 6x \) to both sides:
- \( 4 = 3 \) (This is false, hence no solutions.)

From the above analysis, the equations that have no solutions are:

- \( 6x + 4 = 6x + 3 \)
- \( -6x + 4 = -6x + 3 \)

Thus, both \( 6x + 4 = 6x + 3 \) and \( -6x + 4 = -6x + 3 \) have no solutions. However, since you are looking for a single equation, either of those can be the correct answer depending on which one you want to highlight.

The two equations with no solutions are:
- **\( 6x + 4 = 6x + 3 \)** (also indicated, but just one is needed)
- **\( -6x + 4 = -6x + 3 \)**

Choose one of them based on your required answer.

Answer 4

The first equation you provided that has no solutions is:

**\( 6x + 4 = 6x + 3 \)**

This equation is the simplest and directly shows that \( 4 = 3 \), which is false, thus it has no solutions.

You could also mention the second equation \( -6x + 4 = -6x + 3 \) as it also has no solutions, but according to your request for just one, the most straightforward answer is:

**\( 6x + 4 = 6x + 3 \)**.

Answer 5

Thank you for providing the clear answer choices. Let's evaluate each option to see which has no solutions:

1. **\( 6x + 4 = 6x + 3 \)**
- Subtract \( 6x \) from both sides:
\( 4 = 3 \)
- This is false. **No solutions.**

2. **\( 6x + 3 = -6x + 3 \)**
- Add \( 6x \) to both sides:
\( 12x + 3 = 3 \)
- Subtract \( 3 \) from both sides:
\( 12x = 0 \)
- Thus, \( x = 0 \). **This has a solution.**

3. **\( 6 + 4 = 6x + 4 \)**
- This should probably read \( 6x + 4 = 6 + 4 \).
- If we rewrite it:
- \( 6x + 4 = 10 \)
- Subtract \( 4 \) from both sides:
\( 6x = 6 \)
- Thus, \( x = 1 \). **This has a solution.**

4. **\( -6x + 4 = -6x + 3 \)**
- Add \( 6x \) to both sides:
\( 4 = 3 \)
- This is false. **No solutions.**

### Conclusion

The equations that have **no solutions** from your provided options are:

- **\( 6x + 4 = 6x + 3 \)**
- **\( -6x + 4 = -6x + 3 \)**

Since you need to choose one answer, the first option is the most straightforward:

**\( 6x + 4 = 6x + 3 \)**.