# Absolute Value Inequalities - Concept

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

work.

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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