What is 1<|3x-4/3 |<2 ?

The solution to 1<|3x-4/3 |<2 is -2/9 <x< 1/9 \lor 7/9 <x< 10/9

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1<|3x-4/3 |<2

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

- \frac{2}{9} < x < \frac{1}{9} or \frac{7}{9} < x < \frac{10}{9}

Interval Notation

(- \frac{2}{9}, \frac{1}{9}) \cup (\frac{7}{9}, \frac{10}{9})

Decimal Notation

- 0.22222 \dots < x < 0.11111 \dots or 0.77777 \dots < x < 1.11111 \dots

Solution steps

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

a < u < b

then

a < u and u < b

1 < 3 x - \frac{4}{3} and 3 x - \frac{4}{3} < 2

1 < 3 x - \frac{4}{3} : x < \frac{1}{9} or x > \frac{7}{9}

3 x - \frac{4}{3} < 2 : - \frac{2}{9} < x < \frac{10}{9}

Combine the intervals

(x < \frac{1}{9} or x > \frac{7}{9}) and - \frac{2}{9} < x < \frac{10}{9}

Merge Overlapping Intervals

- \frac{2}{9} < x < \frac{1}{9} or \frac{7}{9} < x < \frac{10}{9}

4 < x^{2} \leq 16

- 1 < x + 1 < 5

x - 5 < - 3 x < x - 1

10 < x - 11 < 13

- 5 < 2 x + 3 < 17

What is 1<|3x-4/3 |<2 ?
The solution to 1<|3x-4/3 |<2 is -2/9 <x< 1/9 \lor 7/9 <x< 10/9