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Popular >

(x-4)/(x+5)<4

Solution

\frac{x - 4}{x + 5} < 4

Solution

x < - 8 or x > - 5

+1

Interval Notation

(- \infty, - 8) \cup (- 5, \infty)

Solution steps

\frac{x - 4}{x + 5} < 4

Rewrite in standard form

\frac{- 3 x - 24}{x + 5} < 0

Factor

\frac{- 3 x - 24}{x + 5} : \frac{- 3 ( x + 8 )}{x + 5}

\frac{- 3 ( x + 8 )}{x + 5} < 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - 3 ( x + 8 ) ) ( - 1 )}{x + 5} > 0 \cdot (- 1)

Simplify

\frac{3 ( x + 8 )}{x + 5} > 0

Divide both sides by

3

\frac{\frac{3 ( x + 8 )}{x + 5}}{3} > \frac{0}{3}

Simplify

\frac{x + 8}{x + 5} > 0

Identify the intervals

x < - 8 or x > - 5

Popular Examples

5 x^{2} + 10 x - 3 = 0

2 x^{2} - 8 x + 3 = 0

simplify (1/81)^{-3/4}simplify

(\frac{1}{81})^{- \frac{3}{4}}

d^{2} + 9 = 0

7 x^{2} - 28 x = 0

Frequently Asked Questions (FAQ)

What is (x-4)/(x+5)<4 ?
The solution to (x-4)/(x+5)<4 is x<-8\lor x>-5