0<|2-3x|<1

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

Solution

0 < ∣ 2 - 3 x ∣ < 1

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

Interval Notation

(\frac{1}{3}, \frac{2}{3}) \cup (\frac{2}{3}, 1)

Decimal Notation

0.33333 \dots < x < 0.66666 \dots or 0.66666 \dots < x < 1

Solution steps

0 < ∣ 2 - 3 x ∣ < 1

a < u < b

then

a < u and u < b

0 < ∣ 2 - 3 x ∣ and ∣ 2 - 3 x ∣ < 1

0 < ∣ 2 - 3 x ∣ : x < \frac{2}{3} or x > \frac{2}{3}

∣ 2 - 3 x ∣ < 1 : \frac{1}{3} < x < 1

Combine the intervals

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

Merge Overlapping Intervals

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

4 \cdot \frac{3 π}{2}

- 4 - 6 y \geq 26

9 x^{2} + 21 x - 8

\frac{x}{3} - 5 = 4

\frac{x - 1}{x - 2} > x