Math Problem Statement

Write a compound inequality for the graph shown below. Use x for your variable.

Solution

From the graph shown in the image, we observe the following intervals:

  • There is an open circle at x=2x = 2, meaning xx cannot equal 2.
  • There is a filled-in circle at x=5x = 5, indicating that x=5x = 5 is included in the solution.
  • The line between x=2x = 2 and x=5x = 5 is shaded, meaning xx is in the interval between 2 and 5.

Thus, the compound inequality represented by this graph is: 2<x52 < x \leq 5

Would you like more details, or do you have any further questions?

Here are 5 related questions:

  1. How do open and closed circles affect inequalities on a graph?
  2. Can you explain the difference between "and" and "or" in compound inequalities?
  3. How can you graph a solution set of inequalities on a number line?
  4. What does it mean when an inequality is strict versus non-strict?
  5. How do we solve inequalities involving absolute values?

Tip: When solving compound inequalities, always pay close attention to whether the inequality includes the boundary values or not (open vs. closed circles).

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Math Problem Analysis

Mathematical Concepts

Inequalities
Compound Inequality
Number Line Representation

Formulas

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Theorems

Properties of Inequalities

Suitable Grade Level

Grades 6-8