https://file.aiquickdraw.com/mathbot/file/1726540507279ekfgu24u.jpg

Yes, the explanation given is correct.

The equation in question is \( |8x - 3| = -2 \).

### Key point:
- Absolute values represent **distance**, and distances cannot be negative. Therefore, the absolute value of any expression is always **non-negative**, meaning it must be either zero or positive. In this case, the right-hand side of the equation is **-2**, which is a negative number.

### Why there is no solution:
- Since an absolute value cannot be equal to a negative number, it is **impossible** for \( |8x - 3| \) to equal \(-2\). Hence, there are **no solutions** to this equation.

This is the reasoning provided in the answer on the paper, and it is accurate.

### Do you have any further questions or need more details? 

Here are five related questions to expand on this concept:
1. What are the steps to solve an absolute value equation when the result is a positive number?
2. How would the equation change if the right-hand side were a positive value, like \( |8x - 3| = 2 \)?
3. What does the graph of an absolute value function look like?
4. How do you interpret absolute value inequalities, such as \( |8x - 3| \geq 2 \)?
5. Can absolute value expressions ever equal zero? If so, under what conditions?

**Tip:** When dealing with absolute value equations, always first check if the given number on the right-hand side is negative. If it is, the equation has no solution.

Explain why the equation |8x - 3| = -2 has no solutions.

Explore why the absolute value equation |8x - 3| = -2 has no solution. This problem delves into key algebraic concepts, including the properties of absolute values, where absolute values represent distance, which cannot be negative. Learn why this equation has no solutions and strengthen your understanding of absolute value equations, suitable for students in Grades 9-11.

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