What is 2-x<= (5x+6)/(x+3) ?

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2-x<= (5x+6)/(x+3)

2 - x \leq \frac{5 x + 6}{x + 3}

- 6 \leq x < - 3 or x \geq 0

Interval Notation

[- 6, - 3) \cup [0, \infty)

Solution steps

2 - x \leq \frac{5 x + 6}{x + 3}

Rewrite in standard form

\frac{- x ^{2} - 6 x}{x + 3} \leq 0

Factor

\frac{- x ^{2} - 6 x}{x + 3} : \frac{- x ( x + 6 )}{x + 3}

\frac{- x ( x + 6 )}{x + 3} \leq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - x ( x + 6 ) ) ( - 1 )}{x + 3} \geq 0 \cdot (- 1)

Simplify

\frac{x ( x + 6 )}{x + 3} \geq 0

Identify the intervals

- 6 \leq x < - 3 or x \geq 0

- 7 x + 7 (- 2 x + 25) = - 56

- 4 u < - 20

(x + 9)^{2} = - 6

((- 4)^{2})^{\frac{1}{2}}

What is 2-x<= (5x+6)/(x+3) ?
The solution to 2-x<= (5x+6)/(x+3) is -6<= x<-3\lor x>= 0