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!