https://file.aiquickdraw.com/mathbot/file/1726773779105kvhssl5f.jpg

The equation in the image is:

\[
|3x - 5| = |-2x - 15|
\]

To solve this, we need to consider the properties of absolute values. When solving equations with absolute values, we must account for two cases:

### Case 1: The expressions inside the absolute values are equal.
\[
3x - 5 = -2x - 15
\]

Solve for \( x \):
1. Add \( 2x \) to both sides:
   \[
   3x + 2x - 5 = -15
   \]
   \[
   5x - 5 = -15
   \]
2. Add 5 to both sides:
   \[
   5x = -10
   \]
3. Divide by 5:
   \[
   x = -2
   \]

### Case 2: The expressions inside the absolute values are negatives of each other.
\[
3x - 5 = -( -2x - 15)
\]

Simplify the right-hand side:
\[
3x - 5 = 2x + 15
\]

Solve for \( x \):
1. Subtract \( 2x \) from both sides:
   \[
   x - 5 = 15
   \]
2. Add 5 to both sides:
   \[
   x = 20
   \]

### Conclusion:
The solution set is \( \{-2, 20\} \), which matches option **B**.

Would you like further details or clarifications? Here are five related questions:

1. How do absolute values affect the structure of equations?
2. Can you explain how to solve absolute value inequalities?
3. What are the general steps for solving an equation with multiple absolute values?
4. What happens if an absolute value equation has no solution?
5. Can absolute value equations have infinitely many solutions?

**Tip:** Always break absolute value equations into cases to handle both positive and negative scenarios.

What is the solution set of the equation |3x - 5| = |-2x - 15|?

This page provides a step-by-step solution for solving the absolute value equation |3x - 5| = |-2x - 15|. The solution involves breaking the equation into two cases: one where the expressions are equal and another where they are negatives of each other. This method helps find the solution set { -2, 20 }, making it a suitable example 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