Which of the following equations have no solutions?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)   \[14x-23=14x-23\]
A
\[14x-23=14x-23\]
(Choice B)   \[-23x-14=14x-23\]
B
\[-23x-14=14x-23\]
(Choice C)   \[-14x+23=14x-23\]
C
\[-14x+23=14x-23\]
(Choice D)   \[14x+23=14x-23\]
D
\[14x+23=14x-23\]

Let's analyze each equation one by one to determine whether they have solutions.

### (Choice A) \(14x - 23 = 14x - 23\)
- Subtract \(14x\) from both sides:
  \[
  -23 = -23
  \]
  This is a true statement, which means this equation is an identity and has infinitely many solutions.

### (Choice B) \(-23x - 14 = 14x - 23\)
- Add \(23x\) to both sides:
  \[
  -14 = 37x - 23
  \]
- Add 23 to both sides:
  \[
  9 = 37x
  \]
- Divide both sides by 37:
  \[
  x = \frac{9}{37}
  \]
  This equation has a solution, so it is **not** a case of no solutions.

### (Choice C) \(-14x + 23 = 14x - 23\)
- Add \(14x\) to both sides:
  \[
  23 = 28x - 23
  \]
- Add 23 to both sides:
  \[
  46 = 28x
  \]
- Divide both sides by 28:
  \[
  x = \frac{46}{28} = \frac{23}{14}
  \]
  This equation has a solution, so it is **not** a case of no solutions.

### (Choice D) \(14x + 23 = 14x - 23\)
- Subtract \(14x\) from both sides:
  \[
  23 = -23
  \]
  This is a false statement, which means this equation has no solutions.

### Conclusion:
The equation that has no solutions is:
- **Choice D: \(14x + 23 = 14x - 23\)**

Would you like more details on how the equations were solved, or do you have any other questions?

Here are 5 relative questions:
1. How do you solve equations with variables on both sides?
2. What does it mean when an equation is an identity?
3. How can you tell if an equation has no solutions?
4. What are the steps to isolate the variable in an equation?
5. Can you have multiple solutions for a linear equation?

**Tip:** When solving equations, always check if simplifying both sides results in a true statement (identity), a false statement (no solution), or a specific solution.

Learn how to identify equations with no solutions by analyzing examples such as 14x-23=14x-23, -23x-14=14x-23, -14x+23=14x-23, and 14x+23=14x-23. Understand the concepts of identities and no solutions in linear equations. Suitable for Grades 7-9 students.

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