The problem presented is:

$|4x + 5| = 1$

This equation involves an absolute value, which means we need to consider two possible cases for solving it:

Case 1: $4x + 5 = 1$

1. Subtract 5 from both sides: $4x = 1 - 5$ $4x = -4$
2. Divide both sides by 4: $x = -1$

Case 2: $4x + 5 = -1$

1. Subtract 5 from both sides: $4x = -1 - 5$ $4x = -6$
2. Divide both sides by 4: $x = -\frac{3}{2}$

So, the solutions are $x = -1$ and $x = -\frac{3}{2}$.

The correct answer is:

A. The solution(s) is/are $x = -1, -\frac{3}{2}$.

Would you like more details on this solution or have any questions?

Follow-up Questions:

1. What are the steps to solve an equation involving absolute value?
2. How do you verify the solutions for an absolute value equation?
3. What would happen if the absolute value equation had a zero on the right side?
4. How would you graph the solutions on a number line?
5. What if the equation had a greater-than inequality instead of an equal sign?

Tip:

Always check both potential cases when solving absolute value equations, as they represent different conditions that the original equation can satisfy.