What is 3/x >= 1/2+4/(x^2) ?

The solution to 3/x >= 1/2+4/(x^2) is 2<= x<= 4

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3/x >= 1/2+4/(x^2)

\frac{3}{x} \geq \frac{1}{2} + \frac{4}{x ^{2}}

2 \leq x \leq 4

Solution steps

\frac{3}{x} \geq \frac{1}{2} + \frac{4}{x ^{2}}

Rewrite in standard form

\frac{6 x - 8 - x ^{2}}{x ^{2}} \geq 0

Factor

\frac{6 x - 8 - x ^{2}}{x ^{2}} : \frac{- ( x - 2 ) ( x - 4 )}{x ^{2}}

\frac{- ( x - 2 ) ( x - 4 )}{x ^{2}} \geq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( x - 2 ) ( x - 4 ) ) ( - 1 )}{x ^{2}} \leq 0 \cdot (- 1)

Simplify

\frac{( x - 2 ) ( x - 4 )}{x ^{2}} \leq 0

Identify the intervals

2 \leq x \leq 4

3 x^{3} - 4 x^{2} + 11 x + 10

\frac{3}{8} + \frac{b}{3} > \frac{5}{12}

3 x^{2} - 9 x \geq 0

\frac{10 !}{5 ! \cdot 5 !}

\frac{2 π}{\frac{5 π}{4}}