https://file.aiquickdraw.com/mathbot/file/1729992508311qna3x392.jpg

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.

Solve the absolute value equation: |4x - 5| + 6 = 4

Learn how to solve the absolute value equation |4x - 5| + 6 = 4 with a step-by-step solution. This problem explores absolute value properties, simplifying techniques, and how to determine if a solution exists. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation