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

The solution to 1<|((x+1))/((x+2))|<3 is x<-5/2 \lor-7/4 <x<-3/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

1<|((x+1))/((x+2))|<3

1 < \frac{( x + 1 )}{( x + 2 )} < 3

x < - \frac{5}{2} or - \frac{7}{4} < x < - \frac{3}{2}

Interval Notation

(- \infty, - \frac{5}{2}) \cup (- \frac{7}{4}, - \frac{3}{2})

Decimal Notation

x < - 2.5 or - 1.75 < x < - 1.5

Solution steps

1 < \frac{( x + 1 )}{( x + 2 )} < 3

a < u < b

then

a < u and u < b

1 < \frac{( x + 1 )}{( x + 2 )} and \frac{( x + 1 )}{( x + 2 )} < 3

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

\frac{x + 1}{x + 2} < 3 : x < - \frac{5}{2} or x > - \frac{7}{4}

Combine the intervals

(x < - 2 or - 2 < x < - \frac{3}{2}) and (x < - \frac{5}{2} or x > - \frac{7}{4})

Merge Overlapping Intervals

x < - \frac{5}{2} or - \frac{7}{4} < x < - \frac{3}{2}

- 1 \leq \frac{( x - 2 )}{( x + 7 )} \leq 1

\frac{- 25}{6} < \frac{1}{2} - 2 \frac{x}{3} < 2

\frac{- 1}{2} < \frac{x}{( x ^{2} - x - 1 )} < 2

- 1 < \frac{( x + 2 )}{( x - 1 )} \leq 1

x + 1 < 3 x - 5 < 4 x - 7

What is 1<|((x+1))/((x+2))|<3 ?
The solution to 1<|((x+1))/((x+2))|<3 is x<-5/2 \lor-7/4 <x<-3/2