This week in math, we started learning about graphing inequalities.

First, we looked at an inequality like . Since we already know about graphing normal equations that equal to 0, we know how to graph 

With that, we know how to find the x-intercepts of the inequality just because of our past knowledge, we use factored form. When factored, the inequality = (x+5)(x-2)>0 so we know that the x-intercepts are x=-5 and x=2.

We can know create a number line to express the 2 known points of this graph: 

Now, we need to find WHEN the graph is greater than 0 as the inequality expresses, so we can use test intervals. This is basically inserting a number as x from the three sections of our x-axis that we have created with our 2 points. We need a number less than -5, a number in between -5 and 2, and then the third will be greater than 2. We do these tests to see if the number that is given after the calculations makes the inequality true. If it is true, we know that is the part of the graph were the inequality is true.

Test intervals:
x = -10 (x<-5)

 

 

 

TRUE

x=0 (-5<x<2)

 

FALSE

x=10 (x>2)

 

 

TRUE

With this information, we can conclude that our solutions are that the inequality is true when x>2 and when x<-5