How do you solve the inequality #9x^2+16>=24x# and write your answer in interval notation?

1 Answer
Binayaka C.
May 25, 2017

Solution: # x in RR # , In Interval notation: #(-oo,oo) #

Explanation:

#9x^2+16>= 24x or 9x^2+16- 24x >=0 or 9x^2- 24x+16 >=0 # or

# (3x-4)^2 >=0 or (3x-4)(3x-4) >=0#. Critical point is # x = 4/3#

At #x =4/3 ; (3x-4)(3x-4) =0#.On either side of #x=4/3 ; (3x-4)(3x-4) >0 :. x in RR # , In Interval notation: #(-oo,oo) #

Solution: # x in RR # , In Interval notation: #(-oo,oo) #
graph{9x^2-24x+16 [-10, 10, -5, 5]} [Ans]

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