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The given equation is \( |5x - 8| = -3 \).

Let's analyze this step by step:

### Key Point:
An absolute value equation is written in the form \( |A| = B \). The absolute value of any expression, by definition, represents a non-negative number. Therefore, it cannot be equal to a negative value. 

In this case, the equation asks for the absolute value \( |5x - 8| \) to be equal to \(-3\), which is impossible because the absolute value of any number or expression cannot be negative.

### Conclusion:
There is **no solution** to this equation. The correct answer is **E. No solution**.

Would you like further clarification or additional examples?

### Related Questions:
1. What would be the solution if the right-hand side was a positive number, say \( |5x - 8| = 3 \)?
2. How do you solve a general absolute value equation \( |A| = B \) when \( B \geq 0 \)?
3. What happens if you remove the absolute value signs from \( |5x - 8| = -3 \)? Would there be a solution then?
4. Can an absolute value equation ever have more than two solutions?
5. How would you solve \( |5x - 8| = 0 \)?

### Tip:
Always check if the value on the right side of the absolute value equation is negative. If it is, the equation has no solution!

Solve the absolute value equation: |5x - 8| = -3

Understand why the absolute value equation |5x - 8| = -3 has no solution. This problem highlights the concept that the absolute value of any number or expression cannot be negative. Suitable for students in Grades 7-9.

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