What is (x+14)/(x+2)>= 3 ?

The solution to (x+14)/(x+2)>= 3 is -2<x<= 4

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(x+14)/(x+2)>= 3

\frac{x + 14}{x + 2} \geq 3

- 2 < x \leq 4

Interval Notation

(- 2, 4]

Solution steps

\frac{x + 14}{x + 2} \geq 3

Rewrite in standard form

\frac{- 2 x + 8}{x + 2} \geq 0

Factor

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

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Divide both sides by

2

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

Simplify

\frac{x - 4}{x + 2} \leq 0

Identify the intervals

- 2 < x \leq 4

4 - 5 x \leq 1

\frac{1}{( \frac{1}{3} )}

25 w^{2} - 20 w + 4

12 x^{2} - 27

3 x^{2} + 22 x - 16