Slide 1

Graphing Inequalities Part 1

Based on what you learned in the video, what can the length of the soccer field be under the restriction L is greater than or equal to 90? Check all of the following dimensions that fit within the inequality.

Description of quiz area:
There are seven answer choices.

1. 92 meters
2. 86 meters
3. Ninety and one tenth meters
4. 101 meters
5. 90 meters
6. 118 meters
7. Eighty-nine and nine tenths meters

Image Description: The outline of a soccer field

The correct answers are:

1. 92 meters
2. Ninety and one tenth meters
3. 101 meters
4. 90 meters
5. 118 meters

Slide 2

Are these all the lengths that are greater than 90 meters? There are actually an infinite number of lengths that are greater than 90 meters! It would take forever to list them all! Instead, we can graph the solutions.

First, we need a number line.

Image Description: A number line extending from negative ten to ten, counting in increments of one with only the even integers showing.

(text on slide) However, this number line won’t do. We need to draw the number line so it displays the number shown in the inequality. This one is better:                    

Image Description: A number line extending from eight-five to ninety-five, counting in increments of one.

 
Slide 3

The arrows at the end of the number line show that it extends forever in each direction. To show all the solutions to the inequality L is greater than or equal to 90, we put a solid dot on the 90 to indicate that 90 is an acceptable length for our soccer field.

Image Description: A number line extending from eight-five to ninety-five, counting in increments of one. A point marks a value of ninety.

(text on slide) Then, we shade all the values that are in the solution set of our inequality. In the case of the length of the soccer field, we shade all the numbers greater than 90 because the soccer field’s length can be any dimension greater than 90.                

Image Description: A number line extending from eight-five to ninety-five, counting in increments of one. A point marks a value of ninety, and a ray marks all values equal to 90 and greater.

(text on slide) Be sure to put an arrow at the end of the shading. The number line shows numbers up to 95, but it actually continues to infinity. By putting an arrow on the end of the shading, we are signifying that we want all the numbers to the right of 90. That is, we want all the numbers greater than 90, such as 98, 105, one hundred two and twenty-five hundredths, etc.             

Slide 4

You have finished this part of the activity.
Return to the main activity to continue.