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

The solution to 1/2 <| x/3+1|<1 is -6<x<-9/2 \lor-3/2 <x<0

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

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

- 6 < x < - \frac{9}{2} or - \frac{3}{2} < x < 0

Interval Notation

(- 6, - \frac{9}{2}) \cup (- \frac{3}{2}, 0)

Decimal Notation

- 6 < x < - 4.5 or - 1.5 < x < 0

Solution steps

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

a < u < b

then

a < u and u < b

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

\frac{1}{2} < \frac{x}{3} + 1 : x < - \frac{9}{2} or x > - \frac{3}{2}

\frac{x}{3} + 1 < 1 : - 6 < x < 0

Combine the intervals

(x < - \frac{9}{2} or x > - \frac{3}{2}) and - 6 < x < 0

Merge Overlapping Intervals

- 6 < x < - \frac{9}{2} or - \frac{3}{2} < x < 0

\frac{- 20}{7} < 3 z + 6 < \frac{- 11}{5}

- 1 \leq \frac{( 2 x + 3 )}{5} \leq 3

x - 3 < x - 2 < x - 1

- 2 < 6 - 4 x < 8

- 5 < 2 x + 1 < 7

What is 1/2 <| x/3+1|<1 ?
The solution to 1/2 <| x/3+1|<1 is -6<x<-9/2 \lor-3/2 <x<0