## DarkBlueChocobo one year ago Help with quadratic inequalities

1. DarkBlueChocobo

\[x^2 -6>-5x\]

2. mathstudent55

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

3. DarkBlueChocobo

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

4. mathstudent55

Good

5. DarkBlueChocobo

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

6. mathstudent55

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

7. DarkBlueChocobo

x= -6 x= 1

8. mathstudent55

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.

9. DarkBlueChocobo

|dw:1438830581670:dw|

10. mathstudent55

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

11. mathstudent55

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.

12. mathstudent55

|dw:1438830839108:dw|

13. DarkBlueChocobo

so 3 regions would be negative positive and 0? or

14. mathstudent55

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. |dw:1438830935258:dw|

15. DarkBlueChocobo

so could we test 2?

16. mathstudent55

Yes, you can test 2. Now we test a number from the middle region. Zero is always easy to check.

17. DarkBlueChocobo

|dw:1438831031694:dw|

18. DarkBlueChocobo

|dw:1438831123797:dw|

19. mathstudent55

I tested 2 above. It is from the right region, and it works, sotot he right of 1 it works. |dw:1438831029172:dw|

20. geerky42

Or you can tell by which way parabola opens. For this problem, you have parabola opening upward, so you have left and right region.

21. mathstudent55

Zero does not work, so the middle region does not work, so we do not color it in. |dw:1438831166432:dw|

22. DarkBlueChocobo

So we have (-inf,-6) U (1,inf)?

23. geerky42

Yeah.