Because things aren’t always equal... Inequalities

The Language of Inequalities Inequalities are represented with 4 different symbols. They are: < Less Than > Greater Than ≤ Less Than or Equal To ≥ Greater Than or Equal To

Real Life Examples of Inequalities Some sentences that involve inequalities: James scored at least a 90% on the last test. The temperature was above freezing. You cannot take this test for more than 60 minutes. Mo Williams is less than 6 feet tall.

Real Life Examples of Inequalities Now, let’s write these sentences mathematically James scored at least a 90% on the last test. James score ≥ 90 The temperature was above freezing. Temperature > 32 You cannot take this test for more than 60 minutes. Time taking test ≤ 60 Mo Williams is less than 6 feet tall. Mo Williams < 6

Your turn to write a few… Write down a few “real world” inequalities of your own. Try to use a few different inequality symbols. Think, Pair, Share for 2 minutes…

Inequalities on a Number Line We also need to know how to represent inequalities on a number line. Let’s take the example: “ James scored at least a 90 on the last test.” First, draw and label a number line. You can put the main number in the middle. Put a few numbers on either side of it, like above

Inequalities on a Number Line Then, you must put a circle around the main number. Place the circle right on top of the number line. Sometimes the circle is colored in; sometimes it is an open circle. More on that in a second. Then, shade the number line, either to the left or the right, to include all possible answers, like above

Inequalities on a Number Line Since James scored at least a 90 on the last test, the grades he could have gotten include 90. That means you have to shade the circle around 90 to show that it is possible he scored a 90. But, if the problem said “James scored higher than a 90”, then we know he didn’t get 90, but maybe a 91, 92, 93…etc. In this case, we would keep the circle open around the 90, to show that he couldn’t have gotten a 90. Like this:

Inequalities on a Number Line Here are some short cuts to help you remember when the circles are shaded or left open: Open CircleShaded Circle Greater than > Greater than or equal to ≥ Less than < Less than or equal to ≤

Now it’s your turn… Draw the graph that goes along with these scenarios: 1. You must be at least 54 inches tall to ride Fury 325 at Carowinds. 2. Your lunch cannot be more than $10, since that’s all the money you have in your pocket! 3. Today’s temperature will be less than 80 degrees.