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

The solution to (x+4)/(x-2)>= 3 is 2<x<= 5

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(x+4)/(x-2)>= 3

\frac{x + 4}{x - 2} \geq 3

2 < x \leq 5

Interval Notation

(2, 5]

Solution steps

\frac{x + 4}{x - 2} \geq 3

Rewrite in standard form

\frac{- 2 x + 10}{x - 2} \geq 0

Factor

\frac{- 2 x + 10}{x - 2} : \frac{- 2 ( x - 5 )}{x - 2}

\frac{- 2 ( x - 5 )}{x - 2} \geq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - 2 ( x - 5 ) ) ( - 1 )}{x - 2} \leq 0 \cdot (- 1)

Simplify

\frac{2 ( x - 5 )}{x - 2} \leq 0

Divide both sides by

2

\frac{\frac{2 ( x - 5 )}{x - 2}}{2} \leq \frac{0}{2}

Simplify

\frac{x - 5}{x - 2} \leq 0

Identify the intervals

2 < x \leq 5

\frac{3}{12}

4 (r + 20) = \frac{1}{5} (20 r + 400)

\frac{9}{12}

(x + 3) (x + 4) > 0

- 0.8 b^{2} + 7.4 b + (5.6 b - 0.2 b^{2})