What is -1<((x+2))/((x-1))<= 1 ?

The solution to -1<((x+2))/((x-1))<= 1 is x<-1/2

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-1<((x+2))/((x-1))<= 1

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

x < - \frac{1}{2}

Interval Notation

(- \infty, - \frac{1}{2})

Decimal Notation

x < - 0.5

Solution steps

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

a < u \leq b

then

a < u and u \leq b

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

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

\frac{x + 2}{x - 1} \leq 1 : x < 1

Combine the intervals

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

Merge Overlapping Intervals

x < - \frac{1}{2}

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

- 12 < 4 - 3 \frac{x}{- 5} \leq 2

44 < x < 45

25 < x < 35

5 x - 1 < (x + 1)^{2} < 7 x - 3

What is -1<((x+2))/((x-1))<= 1 ?
The solution to -1<((x+2))/((x-1))<= 1 is x<-1/2