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Popular >

(4x)/(x+7)<x

Solution

\frac{4 x}{x + 7} < x

Solution

- 7 < x < - 3 or x > 0

+1

Interval Notation

(- 7, - 3) \cup (0, \infty)

Solution steps

\frac{4 x}{x + 7} < x

Rewrite in standard form

\frac{- x ^{2} - 3 x}{x + 7} < 0

Factor

\frac{- x ^{2} - 3 x}{x + 7} : \frac{- x ( x + 3 )}{x + 7}

\frac{- x ( x + 3 )}{x + 7} < 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - x ( x + 3 ) ) ( - 1 )}{x + 7} > 0 \cdot (- 1)

Simplify

\frac{x ( x + 3 )}{x + 7} > 0

Identify the intervals

- 7 < x < - 3 or x > 0

Popular Examples

simplify (20.13)/(0.15*0.048)simplify

\frac{20.13}{0.15 \cdot 0.048}

simplify 2sqrt(24/25)+4sqrt(72/27)-2sqrt(16/72)simplify

2 \frac{24}{25} + 4 \frac{72}{27} - 2 \frac{16}{72}

simplify 2(1/3)^{0-1}+4 simplify

2 (\frac{1}{3})^{0 - 1} + 4

expand (t^{3/2}-t^{1/2})^2 expand

(t^{\frac{3}{2}} - t^{\frac{1}{2}})^{2}

x^{2} + 6 = 10

Frequently Asked Questions (FAQ)

What is (4x)/(x+7)<x ?
The solution to (4x)/(x+7)<x is -7<x<-3\lor x>0