Sitting on the Fence

Is he in or out?
OBJECTIVE: To learn how to solve absolute value inequalities
[br]In previous lessons, you learned about [color=#0000ff]inequalities[/color] and how to graph them on the [color=#0000ff]real number line[/color]. Then you learned about the concept of [color=#0000ff]absolute value[/color] and how to solve [color=#0000ff]absolute value equations[/color]. [br][br][i][color=#0000ff]Talking About Inequalities:[/color][/i] https://www.geogebra.org/m/nrpqkpch[i][br][color=#0000ff]Going the Distance:[/color][/i] https://www.geogebra.org/m/fyuu6q6n[br][i][color=#0000ff]Wearing a Smile or a Frown:[/color][/i] https://www.geogebra.org/m/cczmeqjs[br][br]In this lesson, you're going to learn how to solve [color=#0000ff]absolute value inequalities[/color].[br][br]As you have learned previously, there are four variations of inequalities:[br][br][img]data:image/png;base64,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[/img][br]The first applet below illustrates two variations: [color=#0000ff]less than ( < ) [/color]and [color=#0000ff]less than or equal to ( ≤ )[/color]. The second applet deals with the two other variations: [color=#0000ff]greater than ( > )[/color] and [color=#0000ff]greater than or equal to ( ≥ )[/color].[br][br]Interact with the applets for a few minutes. In both applets, feel free to move the [b][color=#9900ff]BIG PURPLE POINTS[/color][/b] wherever you'd like.
LESS THAN INEQUALITIES
GREATER THAN INEQUALITIES
HOW TO SOLVE ABSOLUTE VALUE INEQUALITIES
[br]Step 1. Change the absolute value inequality into an absolute value equation.[br][br]Step 2. Isolate the absolute value expression. Make sure the number on the other side of the equation is positive. If so, continue to Step 3. Other cases will be discussed separately.[br][br]Step 3. Find the left-hand boundary by equating the algebraic equation inside the absolute value symbol to the negative ( − ) of the number on the other side of the equation and solving for x.[br][br]Step 4. Find the right-hand boundary by equating the algebraic equation inside the absolute value symbol to the positive ( + ) of the number on the other side of the equation and solving for x.[br][br]Step 5. The solution set consists of all values of x that are either inside (or equal to) the boundaries for LESS THAN INEQUALITIES ( first applet) or outside (or equal to) to the boundaries for GREATER THAN INEQUALITIES (second applet). "Equal to" applies only when an equal sign accompanies the inequality symbols. These are shown in the applets as solid line boundaries.
TRY IT YOURSELF ...
[br]Solve the following problems first on a separate sheet of paper, then enter your answers in the corresponding boxes. Use the sliders to change the options. A big "[i][color=#ff00ff]Correct!!![/color][/i]" sign will appear if all your entries and settings are correct. Otherwise, you'll have to redo the problem.[br][br]Repeat as many times as needed to master the concept.
In this lesson, you learned how to solve absolute value inequalities.
In future lessons, you'll learn more about real numbers and operations on real numbers. Hope you ENJOYED today's lesson!

Information: Sitting on the Fence