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

1 Answer
EET-AP
Mar 2, 2017

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.

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