Question

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

Answer 1

Answer:

The first alternative is correct

Step-by-step explanation:

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

$\frac{3}{1}+\frac{4}{x}-\frac{x+2}{x}\geq0\\\\\frac{3x+4-(x+2)}{x}\geq0\\\frac{2x+2}{x}\geq0$

Answer 2

Answer:

the first one

Step-by-step explanation:

Express the left side as a single fraction

3 + $\frac{4}{x}$

= $\frac{3x+4}{x}$, hence

$\frac{3x+4}{x}$ ≥ $\frac{x+2}{x}$

Subtract $\frac{3x+4}{x}$ from both sides

0 ≥ $\frac{x+2}{x}$ - $\frac{3x+4}{x}$

0 ≥ $\frac{-2x-2}{x}$

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

0 ≤ $\frac{2x+2}{x}$, hence

$\frac{2x+2}{x}$ ≥ 0