What is ((sqrt(x+5)))/(|1-x|)>1 ?

The solution to ((sqrt(x+5)))/(|1-x|)>1 is -1<x<1\lor 1<x<4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

((sqrt(x+5)))/(|1-x|)>1

\frac{( x + 5 )}{∣ 1 - x ∣} > 1

- 1 < x < 1 or 1 < x < 4

Interval Notation

(- 1, 1) \cup (1, 4)

Solution steps

\frac{x + 5}{∣ 1 - x ∣} > 1

Move

1

to the left side

\frac{x + 5}{∣ 1 - x ∣} - 1 > 0

Simplify

\frac{x + 5}{∣ 1 - x ∣} - 1 : \frac{x + 5 - ∣ 1 - x ∣}{∣ 1 - x ∣}

\frac{x + 5 - ∣ 1 - x ∣}{∣ 1 - x ∣} > 0

Identify the intervals

- 1 < x < 1 or 1 < x < 4

5 - x < 3

x^{2} + x > 1 - 2 x

x - 1 < 7 - x

n - 3 \geq 3 n + 1

x + 6 < x - 6

What is ((sqrt(x+5)))/(|1-x|)>1 ?
The solution to ((sqrt(x+5)))/(|1-x|)>1 is -1<x<1\lor 1<x<4