How do solve #5/x>3# and write the answer as a inequality and interval notation?

1 Answer
Mar 2, 2017

Answer:

#5/3>x# or #color(blue)(x < 5/3)# and #(0,5/3)#

Explanation:

#(5/x>3)# as in equalities, can be multiplied on both sides by #x# then divided on both sides by #3#

#5 > 3x#

#5/3 > x# is the inequality.

The question gives us a hint in answering the interval notation part, because we can see right away that #x = 0# is undefined and so it must be excluded #color(red)((# as an endpoint.

Since there are no negative numbers given, we are not concerned about endpoints less than #0#.

We can also see from our solution above that #5/3 = x# cannot exist so 5/3 is an excluded #color(red))# endpoint.

Then the interval notation is #(0,5/3)#.

This means x can be #1# or any fraction between #0# and #5/3#, but it cannot be #0# or #5/3#.

Note that when you reverse components in the equality from one side to #color(blue)(the other side)# as in the answer above, it is necessary to REVERSE the sign of the inequality at the same time.