solve the inequality 21/(15-3x) < 0, and express the solution as an interval.?

Question

Possible Solutions:
a) (5, infinity)
b) (7, infinity)
c) (- infinity, 5)
d) (- infinity, 7)

Answer 1

a)
5 < x

Answer 2

21/(15-3x)=7/(5-x)
7/(5-x)<0
The critical point(s) is/are x=5 since the LHS is undefined when you plug in x=5.
Draw the number line out and you try a number larger than 5 and a number smaller than 5.
Try 10 and 0.
10 works but not 0.
So the solution is:
a) (5, infinity)
^_^

Answer 3

If the fraction is negative, the denominator must be negative since the numerator is a constant positive

for the denom to be negative, 15-3x<0 or 15<3x or
5
the solution is that 55 so the interval is (5, inf)

check this by substituting any number larger than five into your original expression; you will see that the denom is neg and the entire fraction is neg

Answer 4

21/(15 - 3x) < 0

Because the numerator is positive, you know that the denominator must be negative if the entire fraction is going to be less than 0.

15 - 3x < 0

15 < 3x

5 < x

x > 5

Therefore the answer is a) (5, infinity)

Answer 5

21/(15-3x)<0
15-3x=0
x=+5
++ - - - -
-----..----------------
+5
in equality <0 so we use - - -
and the answer is x>5

C

Answer 6

15 - 3x < 0
3x > 15
x > 5