Which of the following equations have no solutions?
Choose all answers that apply:
a)-4x+5=-4x-4 b)-4x+5=-4x-5 c) 4x+5=-4x+5 d) 5x+5=-4x-5

Let's analyze each equation to determine if there are no solutions:

**(a) \(-4x + 5 = -4x - 4\)**  
- Simplify by adding \(4x\) to both sides:
  \[
  5 = -4
  \]
- This is a contradiction, which means there are **no solutions**.

**(b) \(-4x + 5 = -4x - 5\)**  
- Simplify by adding \(4x\) to both sides:
  \[
  5 = -5
  \]
- This is also a contradiction, so there are **no solutions**.

**(c) \(4x + 5 = -4x + 5\)**  
- Add \(4x\) to both sides:
  \[
  8x + 5 = 5
  \]
- Subtract 5 from both sides:
  \[
  8x = 0
  \]
- Divide by 8:
  \[
  x = 0
  \]
- This equation has a solution, \(x = 0\).

**(d) \(5x + 5 = -4x - 5\)**  
- Add \(4x\) to both sides:
  \[
  9x + 5 = -5
  \]
- Subtract 5 from both sides:
  \[
  9x = -10
  \]
- Divide by 9:
  \[
  x = -\frac{10}{9}
  \]
- This equation has a solution, \(x = -\frac{10}{9}\).

**Conclusion:**
The equations with no solutions are **(a) \(-4x + 5 = -4x - 4\)** and **(b) \(-4x + 5 = -4x - 5\)**.

Would you like a more detailed explanation of any step or have any questions?

### Related Questions
1. What does it mean for an equation to have no solutions?
2. Can you give an example of an equation that has infinitely many solutions?
3. How can we determine if an equation is inconsistent?
4. How do we check if an equation has exactly one solution?
5. What are the differences between inconsistent and consistent equations?

**Tip:** If simplifying an equation results in a contradiction (e.g., \(5 = -5\)), it means there are no solutions.

Which of the following equations have no solutions? Choose all answers that apply: a) -4x+5=-4x-4 b) -4x+5=-4x-5 c) 4x+5=-4x+5 d) 5x+5=-4x-5

This page provides a step-by-step solution to determine which linear equations have no solutions. It includes examples such as -4x+5=-4x-4 and -4x+5=-4x-5, covering key algebraic concepts for students in Grades 8-10.

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