The given equation is:

$|4x + 5| - 3 = 25$

Solution Steps:

1. Isolate the absolute value expression: $|4x + 5| = 25 + 3$ $|4x + 5| = 28$

2. Set up two cases to remove the absolute value: Since $|4x + 5| = 28$, we have:

   • Case 1: $4x + 5 = 28$
   • Case 2: $4x + 5 = -28$

3. Solve for $x$ in each case:

   • Case 1: $4x + 5 = 28$ $4x = 28 - 5$ $4x = 23$ $x = \frac{23}{4}$

   • Case 2: $4x + 5 = -28$ $4x = -28 - 5$ $4x = -33$ $x = \frac{-33}{4}$

Final Answer:

The exact solutions for $x$ are: $x = \frac{23}{4} \quad \text{and} \quad x = \frac{-33}{4}$

Would you like more details or have any questions?

Here are some related questions:

1. How do you solve other types of absolute value equations?
2. What are the rules for solving equations involving absolute values?
3. How do you interpret absolute values graphically?
4. What happens if the absolute value equation has no solution?
5. Can absolute values be used in inequalities as well?

Tip: Remember, when solving absolute value equations, always consider both the positive and negative cases.