Inequalities

Today in class we got introduced to the solving and graphing of inequalities.

Example 1:
You must be at least 35 inches tall in order to ride Pirate's Lagoon.
Since "at least 35 inches" includes everyone who is exactly 35 inches, the inequality should show that x equals or is greater than 35.

Graphing Inequalities: Inequalites can be graphed on number lines. A filled-in circle means that the number that it is over is included in the set of numbers, and a blank circle means the number isn't included. For example, using the previous example, 35 would have a circle over it, and was filled in. If instead the situation read that you must be taller than 35 inches, exactly 35 inches isn't included. Therefore, the circle above it on a number line would not be shaded in.

Solving Inequalites: Inequalites can be solved the same way as equations, which we learned earlier in the year. Only instead of an equal sign, you have a greater than, less than, equal to or greater than, or equal to or less than.

IMPORTANT!!!!!!!!!!!!!!!!!!!!
When you multiply or divide an inequality by a negative number, you must reverse the direction of the inequality symbol.

5>4 true
-5>-4 false
-5<-4 true


Triangle Inequalities: Today we also got to play around with triangle inequalities. We each drew 3 triangles (any size or type) and collected data. We found the lengths of the shortest, medium, and largest sides. We put our information into a table.

We realized that in order to be a triangle, the shortest side and the middle side together had to be larger than the longest side.