To solve the equation $|4x - 5| + 6 = 4$, let's isolate the absolute value expression and then proceed with solving.

Step-by-Step Solution:

1. Isolate the Absolute Value: $|4x - 5| + 6 = 4$ Subtract 6 from both sides: $|4x - 5| = -2$

2. Analyze the Absolute Value: The absolute value of an expression cannot be negative, so $|4x - 5| = -2$ has no solutions.

Conclusion:

The answer is:

• B. There is no solution.

Would you like further clarification or additional details?

Here are 5 related questions for further practice:

1. How would you solve an equation like $|3x + 2| = 5$?
2. What would change if the equation were $|4x - 5| - 6 = 4$?
3. How can you tell if an absolute value equation has no solution?
4. How do you approach equations with two absolute value expressions, like $|x + 2| = |2x - 3|$?
5. What are the steps for solving inequalities involving absolute values?

Tip: When solving absolute value equations, if you end up with a negative result (e.g., $|expression| = -number$), the equation has no solution.