module 2.5 creating and solving compound …...2019/08/27  · you can combine two simple...

You can combine two simple inequalities to create a compound inequality.

There are 2 types of compound inequalities, AND and OR.

First, let’s talk about the AND, also called an INTERSECTION, where both inequalities are true at the same time.

Here are two simple inequalities: x > 2 x is greater than 2(x represents all real numbers) x < 6 x is less than 6

When you combine them, they become: 2 < x < 6 x is greater than 2 AND less than 6

Which is the same as: 6 > x > 2 x is greater than 2 AND less than 6

Module 2.5 – Creating and Solving Compound Inequalities

The graph of x > 2 looks like this:

The graph of x < 6 looks like this:

When you combine them into a compound inequality, the graph is of the overlapping region,and it looks like this:

We use an open circle here to indicate GREATER THANbut not EQUAL TO.

2 < x < 6

We use an open circle here to indicate LESS THANbut not EQUAL TO.

Note the open circles?

The graph of x > –2 looks like this:

The graph of x ≤ 4 looks like this:

When you combine them into a compound inequality, the graph is of the overlapping region,and it looks like this:

–2 < x ≤ 4

We use a solid circle hereto indicate LESS THAN OR EQUAL TO.

We use an open circle here to indicate GREATER THANbut not EQUAL TO.

Note the open & solid circles?

P. 85

There are 3 rules:1) The variable should always be in the middle. 2) ISOLATE IT!3) Whatever operation you perform on it, you must perform on the left & right sides as well.

The graph/solutions is the overlap!

We use a solid circleto indicate EQUAL TO.

Subtract 2 to isolate the X (as well as from the left & right sides), then simplify.

P. 82

P. 82

Note a dot AND a circle?

P. 83

Now let’s talk about the other type of compound inequality called OR or UNION,where only one inequality can be true at a time.

Here are two inequalities: x < 2 x is less than 2(x represents all real numbers) x > 6 x is greater than 6

They can’t both be true at the same time; how can X be both less than 2 and greater than 6?So it’s either one OR the other.

Here are 2 examples.

Note the open & solid circles?

P. 84

Solve each inequality separately – by isolating its variable.

P. 84

Note an open AND a solid circle?

P. 85

P. 85

P. 86

P. 86

The word inclusive means including endpoints, while exclusive means excluding endpoints.

The ball used in a soccer game may not weigh more than 16 ounces or less than 14 ounces at the start of the match. After 1.5 ounces of air were added to a ball, the ball was approved for use in a game.