How do you solve and write the following in interval notation: #(3 − 5x)(3x − 7) ≥ 0#?

1 Answer
Nghi N
Jul 25, 2017

#[3/5, 7/3]#

Explanation:

#f(x) = (3 - 5x)(3x - 7) >= 0#
First, solve f(x) = 0. Solve the 2 binomials:
3 - 5x = 0 --> 5x = 3 --> #x = 3/5#
3x - 7 = 0 --> 3x = 7 --> #x = 7/3#

On the number line, plot the 2 end-points #(3/5)# and #(7/3)#.
Since a = -15 < 0. The parabola graph of f(x) opens downward.
Between the 2 real roots, f(x) > 0, as a part of the graph stays above the x-axis.
Answer:
Close interval #[3/5, 7/3]#

---------------------- 0 ----- #3/5# + + + + + + + + #7/3# -----------------------

Note. The 2 end-points are included in the solution set.

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