Math Problem Statement

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

Solution

The graph provided shows two open circles at x=2x = -2 and x=4x = 4, with shading between these points. Since the circles are open, it indicates that the values at 2-2 and 44 are not included in the solution.

To write a compound inequality for this graph:

2<x<4-2 < x < 4

This inequality means that xx lies between 2-2 and 44, but does not include 2-2 or 44 themselves.

Would you like further explanation or have any questions?

Here are five related questions to expand on this:

  1. How would the inequality change if the circles were closed?
  2. How do you graph an inequality with one side open and the other side closed?
  3. What is the difference between strict and non-strict inequalities in terms of graphing?
  4. How would the graph look if the inequality were 2x4-2 \leq x \leq 4?
  5. How can you solve compound inequalities algebraically?

Tip: Always look at whether the circles are open or closed on the number line to determine whether to use strict (<<) or non-strict (\leq) inequalities.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Inequalities
Compound Inequalities

Formulas

None

Theorems

Properties of inequalities

Suitable Grade Level

Grades 7-9