how do i solve 1/x<2?

Answer 1

1/x < 2

1 < 2x

2x > 1

x > 1/2

interval type : open → x > a → (a,∞)

(1/2, ∞)

Answer 2

One way you can do this is to setup a "related equation."
A related equation is nothing more than the same equation with an equal sign in it, instead of unequal sign.

1/x = 2

Now solve this and you get x = 1/2 or 0.5

Now, plug this into the original equation and you get:

1/(1/2) < 2

You'll notice, this isn't correct.... they are equal. In order for this to be true, the value X must be larger than what would make it equal.

Therefore x > 1/2

Answer 3

1/x < 2
1 < 2x
1/2 < x

Answer 4

1/x<2

If x > 0, then 1 < 2x
x > 1/2
x positive solution: x > 1/2

If x < 0, then 1 > 2x
x < 1/2
x negative solution: x < 0

All solutions: All reals less than 0 or all reals greater than 1/2

Interval notation: (-∞, 0) and (1/2, ∞)