What is (4x)/(3-x)>= 4x ?

The solution to (4x)/(3-x)>= 4x is x<= 0\lor 2<= x<3

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(4x)/(3-x)>= 4x

\frac{4 x}{3 - x} \geq 4 x

x \leq 0 or 2 \leq x < 3

Interval Notation

(- \infty, 0] \cup [2, 3)

Solution steps

\frac{4 x}{3 - x} \geq 4 x

Rewrite in standard form

\frac{- 8 x + 4 x ^{2}}{3 - x} \geq 0

Factor

\frac{- 8 x + 4 x ^{2}}{3 - x} : \frac{4 x ( x - 2 )}{3 - x}

\frac{4 x ( x - 2 )}{3 - x} \geq 0

Divide both sides by

4

\frac{\frac{4 x ( x - 2 )}{3 - x}}{4} \geq \frac{0}{4}

Simplify

\frac{x ( x - 2 )}{3 - x} \geq 0

Identify the intervals

x \leq 0 or 2 \leq x < 3

x^{2} + 6 x > 27

27 p^{3} + 125 z^{3}

- 2 (y + 6) + 6 y = 4 (y - 3)

16 \cdot 9

\frac{\frac{7}{y} + \frac{2}{x}}{- 8 x}