Solving and Graphing Compound Inequalities - Problem 3


Solve "or" compound inequalities individually and graph on the same number line. The resulting graph should have two arrows pointing outwards (away from each other). An "or" inequality means that a possible solution could be less than a certain number OR greater than the other number. For example, x < 8 or x > 16 means that the solution can be less than 8 or greater than 16.


This is a compound inequality that uses the word 'or' so before I even do any Mathy stuff I'm going to think about how my answer on the number line should look like a graph that goes out like this, like oars on a canoe or something, I don't know.

So this is like two different problems, I'm going to solve each one individually and then just graph them together. First thing I would do in this problem to get x all by itself is subtract 3 from both sides. So part of my answer excuse me is x is less than 8. The other part of my answer comes from this problem x is larger than 16. This is my solution written out in symbols, I also want to make sure I graph it.

You want to ask your teacher how precise your graph needs to be. For me I'm a Math teacher I just ask that student to show zero and do it kind of a rough graph it can be a rough estimate. So like I kind of spaced 8 and 16 equally apart. I want numbers where x is less than 8 open circle because it's just less than, it's not less than or equal to and then open circle at 16, x could be a number that's bigger than 16.

So again this is kind of a weird problem because it looks like two different ones but we graph them together. The word 'or' links them together and makes them a compound inequality and the thing that's pretty cool as you say my solutions could be any number that's less than 8 or any number that's bigger that 16. It's like one big long sentence after your solution region but I think this way or this way both demonstrates that pretty simply.

inequality solve compound