How do solve #5/x3# and write the answer as a inequality and interval notation?

Question

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

Liam Brennan · Accepted Answer

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

Xavier Alonso · Answer

undefined To solve $ \frac{5}{x} > 3 $, first, multiply both sides by $ x $ to clear the denominator. Then, solve for $ x $.

$ 5 > 3x $

$ \frac{5}{3} > x $

Inequality notation: $ x < \frac{5}{3} $

Interval notation: $ (-\infty, \frac{5}{3}) $

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

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