What is (20}{x-1}-\frac{20)/x >= 1 ?

The solution to (20}{x-1}-\frac{20)/x >= 1 is -4<= x<0\lor 1<x<= 5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(20}{x-1}-\frac{20)/x >= 1

\frac{20}{x - 1} - \frac{20}{x} \geq 1

- 4 \leq x < 0 or 1 < x \leq 5

Interval Notation

[- 4, 0) \cup (1, 5]

Solution steps

\frac{20}{x - 1} - \frac{20}{x} \geq 1

Rewrite in standard form

\frac{- x ^{2} + x + 20}{x ( x - 1 )} \geq 0

Factor

\frac{- x ^{2} + x + 20}{x ( x - 1 )} : \frac{- ( x + 4 ) ( x - 5 )}{x ( x - 1 )}

\frac{- ( x + 4 ) ( x - 5 )}{x ( x - 1 )} \geq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( x + 4 ) ( x - 5 ) ) ( - 1 )}{x ( x - 1 )} \leq 0 \cdot (- 1)

Simplify

\frac{( x + 4 ) ( x - 5 )}{x ( x - 1 )} \leq 0

Identify the intervals

- 4 \leq x < 0 or 1 < x \leq 5

(2 x + 3)^{2} = 16

205

a + 3 + 2 a = - 1 + 3 a + 4

3 x^{2} + 27 x = 30

\frac{1}{3} + \frac{1}{2} + \frac{1}{4}

What is (20}{x-1}-\frac{20)/x >= 1 ?
The solution to (20}{x-1}-\frac{20)/x >= 1 is -4<= x<0\lor 1<x<= 5