For the following exercises, graph the function. Observe the points of intersection and shade the x-axis representing the solution set to the inequality. Show your graph and write your final answer in interval notation. [3x + 1 > 2x − 5 > x − 7]

The graph shows the solution set for the inequality \(3x + 1 > 2x - 5 > x - 7\). The shaded region to the right of \(-2\) represents the solution, which in interval notation is:
\[
(-2, \infty)
\]

Would you like any further details on this solution or the steps involved? Here are some related questions for further exploration:

1. How would the solution change if one of the inequalities were non-strict, such as \( \geq \)?
2. How do we graph solutions on a number line for inequalities involving \(\leq\) or \(\geq\)?
3. What are compound inequalities, and how do we identify them?
4. How can we solve inequalities involving absolute values?
5. What are the steps for solving compound inequalities with three or more parts?

**Tip:** When solving compound inequalities, treat each part of the inequality separately, then find the intersection of all solution sets for the final answer.

Learn how to graph and solve the compound inequality 3x + 1 > 2x - 5 > x - 7. This problem involves graphing on a number line, simplifying inequalities, and expressing the solution in interval notation. 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