https://file.aiquickdraw.com/mathbot/file/17261099915660lfytd6k.jpg

The graph shows two lines representing \( f(x) \) (blue line) and \( g(x) \) (red line). We are tasked with solving the inequality \( f(x) < g(x) \) using the graph.

### Step-by-step process:
1. **Intersection Point**: The blue line (\( f(x) \)) and red line (\( g(x) \)) intersect at the point \( (2, 4) \).
2. **Behavior of the lines**: 
   - To the left of \( x = 2 \), the blue line (\( f(x) \)) is above the red line (\( g(x) \)). Therefore, \( f(x) > g(x) \) in this region.
   - To the right of \( x = 2 \), the blue line (\( f(x) \)) is below the red line (\( g(x) \)). Therefore, \( f(x) < g(x) \) in this region.
   
### Solution:
The inequality \( f(x) < g(x) \) holds for \( x > 2 \). Therefore, the solution is:
\[
x > 2
\]

Would you like any further explanation or details? Here are five related questions for further practice:

1. How do you find the equation of the lines from the graph?
2. How would the solution change if the inequality was \( f(x) \leq g(x) \)?
3. What is the meaning of the intersection point in terms of \( f(x) = g(x) \)?
4. How can you determine if \( f(x) > g(x) \) in a certain interval using only the graph?
5. How would you solve the inequality if the lines were curved (non-linear)?

### Tip:
When solving inequalities with graphs, always check where the curves or lines intersect, as this is where the sign of the inequality changes.

Solve the inequality f(x) < g(x) using the graph given below.

Learn how to solve the inequality f(x) < g(x) using a graph. This problem involves graphing functions and understanding their relationships based on visual interpretation. The solution shows that f(x) is less than g(x) for values of x greater than 2.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation