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

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x/(x+2)>5

Solution

\frac{x}{x + 2} > 5

- \frac{5}{2} < x < - 2

Interval Notation

(- \frac{5}{2}, - 2)

Decimal Notation

- 2.5 < x < - 2

Solution steps

\frac{x}{x + 2} > 5

Rewrite in standard form

\frac{- 4 x - 10}{x + 2} > 0

Factor

\frac{- 4 x - 10}{x + 2} : \frac{- 2 ( 2 x + 5 )}{x + 2}

\frac{- 2 ( 2 x + 5 )}{x + 2} > 0

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

\frac{2 ( 2 x + 5 )}{x + 2} < 0

Divide both sides by

2

\frac{\frac{2 ( 2 x + 5 )}{x + 2}}{2} < \frac{0}{2}

Simplify

\frac{2 x + 5}{x + 2} < 0

Identify the intervals

- \frac{5}{2} < x < - 2

6 p^{2} - 5 p - 6 = 0

8 = \frac{n}{9}

89

\frac{1 - a}{a ^{2} - a + 1} + \frac{a ^{2}}{a ^{3} + 1}

\frac{1}{1 0 ^{- 3}}