What is 0<|3x+1|< 1/3 ?

The solution to 0<|3x+1|< 1/3 is -4/9 <x<-1/3 \lor-1/3 <x<-2/9

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0<|3x+1|< 1/3

0 < ∣ 3 x + 1 ∣ < \frac{1}{3}

- \frac{4}{9} < x < - \frac{1}{3} or - \frac{1}{3} < x < - \frac{2}{9}

Interval Notation

(- \frac{4}{9}, - \frac{1}{3}) \cup (- \frac{1}{3}, - \frac{2}{9})

Decimal Notation

- 0.44444 \dots < x < - 0.33333 \dots or - 0.33333 \dots < x < - 0.22222 \dots

Solution steps

0 < ∣ 3 x + 1 ∣ < \frac{1}{3}

a < u < b

then

a < u and u < b

0 < ∣ 3 x + 1 ∣ and ∣ 3 x + 1 ∣ < \frac{1}{3}

0 < ∣ 3 x + 1 ∣ : x < - \frac{1}{3} or x > - \frac{1}{3}

∣ 3 x + 1 ∣ < \frac{1}{3} : - \frac{4}{9} < x < - \frac{2}{9}

Combine the intervals

(x < - \frac{1}{3} or x > - \frac{1}{3}) and - \frac{4}{9} < x < - \frac{2}{9}

Merge Overlapping Intervals

- \frac{4}{9} < x < - \frac{1}{3} or - \frac{1}{3} < x < - \frac{2}{9}

- 2 < 8 - 2 x < - 1

2 x < x - 4 \leq 3 x + 8

5 \leq 4 x + 1 \leq 13

- 0.7 < z < 1.3

- 1 < 2 x - 3 < x

What is 0<|3x+1|< 1/3 ?
The solution to 0<|3x+1|< 1/3 is -4/9 <x<-1/3 \lor-1/3 <x<-2/9