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Move the -5x to the left, and factor the left side. What do you get?
so we have to get it to one side If I understand so \[x^2 + 5x -6 > 0\]
(x+6)(x-1) I believe would be the factors
Good. Now pretend it's an equation, and find the zeros. (x + 6)(x - 1) = 0
x= -6 x= 1
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.
Great. Now we write the factored inequality below the number line, so we can use it easily. |dw:1438830704607:dw|
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.
so 3 regions would be negative positive and 0? or
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|
so could we test 2?
Yes, you can test 2. Now we test a number from the middle region. Zero is always easy to check.
I tested 2 above. It is from the right region, and it works, sotot he right of 1 it works. |dw:1438831029172:dw|
Or you can tell by which way parabola opens. For this problem, you have parabola opening upward, so you have left and right region.
Zero does not work, so the middle region does not work, so we do not color it in. |dw:1438831166432:dw|
So we have (-inf,-6) U (1,inf)?