Math Problem Statement

Slice Name Equations and Inequalities Topic Name Writing a compound inequality given a graph on the number line

Write a compound inequality for the graph shown below. Use x for your variable. The number line shows a range between -3 and 3 with filled circles at both endpoints.

Solution

In the given graph, two points are marked on the number line at -3 and 3. Both of these points have filled circles, meaning that the values -3 and 3 are included in the inequality. The shaded portion of the graph appears to cover the range between -3 and 3, indicating that the inequality is bounded between these two points.

The compound inequality is:

3x3-3 \leq x \leq 3

This inequality states that xx is greater than or equal to -3 and less than or equal to 3.


Would you like further details or have any questions on this topic?

Here are 5 related questions to further your understanding:

  1. What is the difference between "and" and "or" in compound inequalities?
  2. How do we represent open and closed intervals on a number line?
  3. Can compound inequalities involve more than two conditions?
  4. How do we solve compound inequalities involving variables on both sides?
  5. What is the relationship between compound inequalities and absolute value inequalities?

Tip: When you see filled circles on a number line, it indicates that the endpoints are included in the inequality (represented by "≤" or "≥").

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Math Problem Analysis

Mathematical Concepts

Compound Inequality
Number Line
Algebra

Formulas

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Theorems

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Suitable Grade Level

Grades 6-8