How do you solve and write the following in interval notation: #x^2+9x+20≥2#?

1 Answer
Noah G
May 30, 2016

Start by solving as a regular quadratic equation (we change the inequality sign to an equal for the time being).

#x^2 + 9x + 20 = 2#

#x^2 + 9x + 18 = 0#

#(x + 6)(x + 3) = 0#

#x = -6 and -3#

Now, we select test points that are at different segments of the number line representation of this inequality, as shown below.

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BLUE SEGMENT: Let the test point be #x = -8#

Testing:

#(-8)^2 + 9(-8) + 20 >=^? 2#

#64 - 72 + 20 >= 2#, therefore this interval satisfies the equation. This instantly means that the pink segment is not a solution to the inequality while the green is. Quick checks yield the same result.

Therefore, in interval notation, the solution set is # (-oo, -6) uuu (-3, oo)#

Hopefully this helps!

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