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Absolute Value Inequalities - Concept

Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

To solve an absolute value inequality, knowledge of absolute values and solving inequalities are necessary. Absolute value inequalities can have one or two variables. Solving and graphing absolute value inequalities with two variables is also a skill that math teachers require students to master in Algebra I.

When you're working with absolute value
inequalities, there's a lot you
gotta keep straight in your brain.
You have to combine everything you know
about inequalities, with everything
you know about absolute values, and then
probably you're going to be asked
to graph things.
So that's like three huge concepts you
gotta keep straight in your brain.
It's okay.
Just make sure you guys are going through
step-by-step and showing all of your

So when you're working with inequalities,
you guys know a few things.
The first thing you know is that if you multiply
or divide by a negative number,
you have to change the direction
of inequality sign.
And we'll see that when you guys start
doing some practice problems.
Again, if you multiply or divide by a negative
number with an inequality you
have to change the direction
of the inequality sign.

The other thing that you guys know about
absolute values is that you're going
to probably have two answers.
Most of the time with absolute
values you get two solutions.
And the way you find those solutions is
by isolating the absolute value tracks
and then splitting.
So your absolute value quantity is equal
to the negative value and also the
positive value.

The last thing you want to keep in mind
is the open circle/closed circle thing.
When you're asked to graph, keep in mind
that open circle on the number line
goes for when you have inequality signs
that are strict inequalities.
A closed circle happens when you have
greater than or equal to or else than
or equal to.

And you'll see all of those three key ideas
come together when you start doing
practice problems.

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