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.