Solving+compound+inequalities +and+vs+or+set+6

What does a compound inequality look like? How is this different from a regular inequality? Give a few examples. Sam Heyman

a compound inequality is as follows 6≤x≤12 this is different because the problem gives a certain place where the answer may be, as opposed to a regular inequality which just gives a broad range. ex. x≥100000000. the compound inequality narrows it down a little bit

8<x<21 -12<x<13

How is solving an "and" statement different from solving an "or" statement? What do you look for in the number line graphs? Remember that an "and" statement is NOT always going to be a "betweenness" and an "or" statement is NOT always going to require that the "outer" parts of the number line are shaded! Give some examples of these more interesting examples.

Give an example of a compound inequality in which the solution is all real numbers. Is it possible to have an "and" statement that yields this result?

--Jeremy Comer

And example of an inequality that satisfies all real numbers would be x≥4 or 5≥x. This is an or statement which means the graph would have to satsify all the requirements of both inequalities. They would overlap in opposite directions, providing a solution that is all real numbers. It is impossible to have an and statement with this result because it must satisfy the requirements that the inequalities have in common. If the inequalties overlap in opposite directions like the one I have posted, it would form a segment between 4 and 5. If they overlap in the same direction for an "and" statement, you only shade what satisfies both inequalities. If they don't have anything in common, then there is no solution.

When is a compound inequality a betweenness? How can you go back and forth between writing the inequality as a betweenness and two separate inequalities?Give a few examples to illustrate.

Sam Heyman- A compound inequality is when there is an inequality such as y≤x≤z and it ends up that the x is in between y and z. you can write these as two equations such as y≤x AND x≤z.... some examples of this are... 6≤x≤9 x≤9 and 6≤x

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In which situation is the solution an intersection of two sets of numbers?Give one example in which the intersection yields a betweenness and one example in which it yields something else!!

In which situation is the solution of union of two sets of numbers? Give one example in which the union yields an "outer ends of the number line" situation and one example in which it yields something else!!