https://file.aiquickdraw.com/mathbot/file/1726450342483ex2nztjj.jpg

The image shows a graph of two absolute value functions, and you're asked to solve the equation:

\[
|3x - 1| = |2x + 1|.
\]

From the graph:

- The red line corresponds to \( y = |3x - 1| \).
- The blue line corresponds to \( y = |2x + 1| \).

To solve the equation, we are looking for the points where these two functions intersect. From the graph, there are two points of intersection:

1. At \( x = 0 \), the two functions intersect at the point \((0, 1)\).
2. The second point of intersection occurs around \( x = 2 \).

Thus, the solutions to the equation \( |3x - 1| = |2x + 1| \) are approximately:

\[
x = 0 \quad \text{and} \quad x = 2.
\]

Would you like further details on solving this algebraically?

Here are some related questions:
1. How do we solve absolute value equations algebraically?
2. Can this method be extended to other similar absolute value equations?
3. Why do absolute value functions create "V" shapes on graphs?
4. What does it mean geometrically when two absolute value functions intersect?
5. How can we verify the solutions graphically and algebraically?

**Tip:** When solving absolute value equations, always check for two cases: when the inside of the absolute value is positive and when it's negative.

Solve the absolute value equation |3x - 1| = |2x + 1| by interpreting the intersection points of two absolute value functions on a graph. Learn key algebraic concepts and graphical solutions, 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