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DarkBlueChocobo
 one year ago
Help with quadratic inequalities
DarkBlueChocobo
 one year ago
Help with quadratic inequalities

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DarkBlueChocobo
 one year ago
Best ResponseYou've already chosen the best response.1\[x^2 6>5x\]

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3Move the 5x to the left, and factor the left side. What do you get?

DarkBlueChocobo
 one year ago
Best ResponseYou've already chosen the best response.1so we have to get it to one side If I understand so \[x^2 + 5x 6 > 0\]

DarkBlueChocobo
 one year ago
Best ResponseYou've already chosen the best response.1(x+6)(x1) I believe would be the factors

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3Good. Now pretend it's an equation, and find the zeros. (x + 6)(x  1) = 0

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3Great. 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
 one year ago
Best ResponseYou've already chosen the best response.1dw:1438830581670:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3Great. Now we write the factored inequality below the number line, so we can use it easily. dw:1438830704607:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3The 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
 one year ago
Best ResponseYou've already chosen the best response.3dw:1438830839108:dw

DarkBlueChocobo
 one year ago
Best ResponseYou've already chosen the best response.1so 3 regions would be negative positive and 0? or

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3Notice 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

DarkBlueChocobo
 one year ago
Best ResponseYou've already chosen the best response.1so could we test 2?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3Yes, you can test 2. Now we test a number from the middle region. Zero is always easy to check.

DarkBlueChocobo
 one year ago
Best ResponseYou've already chosen the best response.1dw:1438831031694:dw

DarkBlueChocobo
 one year ago
Best ResponseYou've already chosen the best response.1dw:1438831123797:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3I tested 2 above. It is from the right region, and it works, sotot he right of 1 it works. dw:1438831029172:dw

geerky42
 one year ago
Best ResponseYou've already chosen the best response.0Or you can tell by which way parabola opens. For this problem, you have parabola opening upward, so you have left and right region.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3Zero does not work, so the middle region does not work, so we do not color it in. dw:1438831166432:dw

DarkBlueChocobo
 one year ago
Best ResponseYou've already chosen the best response.1So we have (inf,6) U (1,inf)?
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