__Solving Absolute Value Equations and Inequalities from a Graphical and Algebraic Point of View.__
I have
struggled with helping my students understand how to solve absolute value
equations and inequalities with only one variable like |2

*x*– 8| = 4, |2*x*– 8| > 4, or |2*x*– 8| < 4. Some of my students in the past have understood it while others have not. Most of the time they forget or do not understand to solve half the problem. The will solve the 2*x*– 8 = 4 or 2*x*– 8 > 4 but not the other halves of those two problems or they do not understand when to use a compound inequalities versus two separate inequalities separated by an “or” statement.
I started
my lesson from scratch and approached the material from a graphical and
algebraic point of view. You can access
my video lesson at https://youtu.be/oSmeu3cwsfY

Below is
an overview of the approach I took with more details in the video. https://youtu.be/oSmeu3cwsfY

**Solve |2**

*x*– 8| = 4 by graphing**Use the above picture and solutions to help students see the solutions for |2**

*x*– 8| > 4, and |2*x*– 8| < 4.

**I follow this with the details of how the algebraic method ties into the graphical and how to get the solutions algebraically.**

Tying in
more than one perspective in our lessons will help students better understand and
make more connections with the mathematical concepts we are trying to help them
learn. It is not easy to make many of
these connections. It takes lot of time
to think and reflection plus time to design an effective lesson but it is well
worth it since it helps our students learn.

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