What is |(2-3x)/(1+x)|>1 ?

The solution to |(2-3x)/(1+x)|>1 is x 3/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

|(2-3x)/(1+x)|>1

\frac{2 - 3 x}{1 + x} > 1

x < - 1 or - 1 < x < \frac{1}{4} or x > \frac{3}{2}

Interval Notation

(- \infty, - 1) \cup (- 1, \frac{1}{4}) \cup (\frac{3}{2}, \infty)

Decimal Notation

x < - 1 or - 1 < x < 0.25 or x > 1.5

Solution steps

\frac{2 - 3 x}{1 + x} > 1

Apply absolute rule: If

∣ u ∣ > a, a > 0

then

u < - a

u > a

\frac{2 - 3 x}{1 + x} < - 1 or \frac{2 - 3 x}{1 + x} > 1

\frac{2 - 3 x}{1 + x} < - 1 or \frac{2 - 3 x}{1 + x} > 1

(x < - 1 or x > \frac{3}{2}) or - 1 < x < \frac{1}{4}

Merge Overlapping Intervals

x < - 1 or - 1 < x < \frac{1}{4} or x > \frac{3}{2}

4 x^{2} - 6 x + 5 = 0

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

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

\frac{8 !}{6 !}

x^{2} + 7 x = 3 x

What is |(2-3x)/(1+x)|>1 ?
The solution to |(2-3x)/(1+x)|>1 is x<-1\lor-1<x< 1/4 \lor x> 3/2