Help with quadratic inequalities

Question

darkbluechocobo · Answer

$$x^2 -6>-5x$$

mathstudent55 · Answer

Move the -5x to the left, and factor the left side.
What do you get?

darkbluechocobo · Answer

so we have to get it to one side If I understand so 

$$x^2 + 5x -6 > 0$$

mathstudent55 · Answer

Good

darkbluechocobo · Answer

(x+6)(x-1) I believe would be the factors

mathstudent55 · Answer

Good.
Now pretend it's an equation, and find the zeros.
(x + 6)(x - 1) = 0

darkbluechocobo · Answer

x= -6
x= 1

mathstudent55 · Answer

Great.
Now we move on to a number line.
Since the inequality sign is strictly >, and not >=, mark open circles on the number line at the zeros of the equation.

darkbluechocobo · Answer

|dw:1438830581670:dw|

mathstudent55 · Answer

Great.
Now we write the factored inequality below the number line, so we can use it easily.
|dw:1438830704607:dw|

mathstudent55 · Answer

The two zeros of the equation are two points of interest for us.
They divide the number line into 3 regions (not counting the points of interest).
Now we pick a number from each region and test in the factored inequality.
If the number works, we darken the entire region the number is in.

mathstudent55 · Answer

|dw:1438830839108:dw|

darkbluechocobo · Answer

so 3 regions would be negative  positive and 0? or

mathstudent55 · Answer

Notice that since we are comparing with zero, if -7 in the two factors is negative, we know negative times negative is positive, so it works. The left region works.
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