SOLUTION: Solve the following inequalities:All intervals in interval notation A) 2x^2>=7x+4 B) (x-2)(x+4)^2 (x-6)<0

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Question 1006754: Solve the following inequalities:All intervals in interval notation
A) 2x^2>=7x+4
B) (x-2)(x+4)^2 (x-6)<0
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
(A):

2x%5E2-7x-4%3E=0
Might be factorable, but going with formula for solution to quadratic formula to get the zeros, x=-1%2F2 OR x=4. The roots will be INCLUDED in the solution to the given inequality because it is an INCLUSIVE inequality.

You can use the zeros as critical values and check the three intervals on the x-axis for each interval's satisfying the inequality; or you can recognize the parabola expression, opens upward, so the values above 0 should occur to the left of the -1%2F2 and or to the right of 4.

Solution is x%3C=-1%2F2 OR x%3E=4.