https://file.aiquickdraw.com/mathbot/file/1730144250689w9ffh4o9.jpg

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.

Learn how to solve the absolute value equation |4x + 5| - 3 = 25 with a detailed step-by-step solution. This problem covers key algebraic concepts and absolute value properties, making it suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation