Question

Which inequality is equivalent to 3+4/x>=x+2/x

Answer 1

the first one

Explanation:

Express the left side as a single fraction

3 +
`(4)/(x)`

=
`(3x+4)/(x)`, hence

`(3x+4)/(x)` ≥
`(x+2)/(x)`

Subtract
`(3x+4)/(x)` from both sides

0 ≥
`(x+2)/(x)` -
`(3x+4)/(x)`

0 ≥
`(-2x-2)/(x)`

Multiply both sides by - 1, remembering to reverse the inequality symbol as a consequence

0 ≤
`(2x+2)/(x)`, hence

`(2x+2)/(x)` ≥ 0

Answer 2

The first alternative is correct

Explanation:

We move all the expressions to the left hand side of the inequality then combine like terms using lcm;

`(3)/(1)+(4)/(x)-(x+2)/(x)\geq0\\\\(3x+4-(x+2))/(x)\geq0\\(2x+2)/(x)\geq0`