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Solving and Graphing Compound Inequalities - Problem 3

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

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.

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