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Algebra 1

2.9.6 Using Technology to Visualize Inequality Solutions

Algebra 12.9.6 Using Technology to Visualize Inequality Solutions

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Activity

Consider the inequality 12x+6<4x312x+6<4x3. Let’s look at another way to find its solutions.

1.

Use the graphing tool or technology outside the course. Graph y=12x+6y=12x+6and y=4x3y=4x3 on the same coordinate plane using the Desmos tool below.

Use your graphs to answer the following questions:

2.

Find the values of 12x+612x+6 and 4x34x3 when xx is 1.

3.

What value of xx makes 12x+612x+6 and 4x34x3 equal?

4.

For what values of xx is 12x+612x+6 less than 4x34x3?

5.

For what values of xx is 12x+612x+6 greater than 4x34x3?

6.

What is the solution to the inequality 12x+6<4x312x+6<4x3? Be prepared to explain how you know.

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© May 21, 2025 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.