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

The solution to 4/(x+3)>= x is x<=-4\lor-3<x<= 1

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4/(x+3)>= x

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

x \leq - 4 or - 3 < x \leq 1

Interval Notation

(- \infty, - 4] \cup (- 3, 1]

Solution steps

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

Rewrite in standard form

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

Factor

\frac{4 - x ( x + 3 )}{x + 3} : \frac{- ( x - 1 ) ( x + 4 )}{x + 3}

\frac{- ( x - 1 ) ( x + 4 )}{x + 3} \geq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( x - 1 ) ( x + 4 ) ) ( - 1 )}{x + 3} \leq 0 \cdot (- 1)

Simplify

\frac{( x - 1 ) ( x + 4 )}{x + 3} \leq 0

Identify the intervals

x \leq - 4 or - 3 < x \leq 1

2 = - 5 x + 3 x^{2}

\frac{( - 1 ) ^{5} ( 3 ) + 5}{- 2}

- 3 x \leq 18

6 x^{2} + 60 x + 150 = 0

\frac{x ^{2}}{5 y} \cdot \frac{25 y ^{3}}{x ^{5}}