When you're graphing inequalities that have both x and y there's a three step process you want to use.
First thing you want to do is graph the line using y=mx+b techniques. What I mean by that is get the y all by itself put a dot at your y intercepts from there count the slope and then connect the line.
Next thing you're going to want to do is adjust the line based on if it's one of these inequalities symbols or one of these, less than and greater than ask that you draw a dotted line because those points actually are not technically solutions. You get solid line if it's one of these inequality symbols.
Lastly any time you're graphing an inequality you're going to have some shading, like remember on the number line how you had to graph going out in the directions are like a dumbbell shape or whatever you had to draw some shading, the same thing is true in the xy plane only you're going to be shading like half the plane think about an xy coordinate plane with a line cutting across it, you're going to be shading either everything on one side of that line or the other side. The way to figure out which way to shade is to pick any point you want to that's not on that line substituting your x and y values to the inequality and you're going to be shading the side of the line that make the inequality true.
So this is a really important three step process you might want to write down on note card or something that you can have next to you when you're doing your homework problems and if you can remember this process and keep it all straight you'll have a lot of success on these problems.
One of the difficult things about inequalities is that sometimes it is like two problems on top of each other, that's what is called a "Compound Inequality." Two inequalities combined into one statement using the word "and" or "or" is called a compound inequality.
And here is a couple of examples, this is like one problem it looks like two problems, this is one problem right here, x is greater than 2 and x is less than 5. Sometimes you'd see it like this, you'll have x in the middle, there is the x is less than 5 piece and I'm, going to combine it with x is greater than 2. It's kind of tricky this is the same thing written in two different ways, here it uses the word and, here it just has the two different inequalities signs. And when you graph an and problem your graph is going to look like a dumbbell. You're going to have two values and you're going to be marking the area in between them.
Or, this is another kind of compound inequality that uses the word or, x is less than 3 or x is greater than 8. It's kind of weird this is just one problem even though it looks like two separate things we graph them together. Like I would have x is less than 3, 0 1 2 3. x is less than 3 or x is bigger than 8, 4 5 6 7 8. x is bigger than 8. This graph is kind of dumbbell shape represents an or compound inequality. And the trick is that you might have and where it looks like a dumbbell or you might have or where it looks like it's going out like I remember it cause it looks like oars like if you were in a boat oars I don't know if that helps you.
But these are the two different types of compound inequalities, one more thing that I want to leave you with is that if you're asked to solve something like this like if it had been x+1 right there you would pretend like there were just two different equal signs. Like if that was x+1 I want to subtract 1, I would subtract 1 here, subtract 1 there and subtract 1 there, so it would look like 1 is less than x is less than 4.
That's a whole another problem and you'll see them more when you get into some solving just keep in mind compound inequalities is like two different problems combined into one if it uses the word and it'll look like a dumbbell, if it uses the word or it'll look like oars like rowing oars.