Solve the inequality: 0<|2-3x|<1

Answer 1

0 < l 2 - 3x l < 1 means that l 2 - 3x l > 0 AND l 2 - 3x l < 1

If l 2 - 3x l < 1, then -1 < 2 - 3x < 1. So, -3 < -3x < -1. 1 > x > 1/3

l 2 - 3x l > 0 for all x ≠ 2/3

Solution set: (1/3, 2/3) ∪ (2/3, 1)

Answer 2

Assuming 2 - 3x is positive

0 < 2 - 3x < 1

-2 < -3x < -1

2/3 > x > 1/3

Assuming 2 - 3x is negative

0 < -(2 - 3x) < 1

0 < -2 + 3x < 1

2 < 3x < 3

2/3 < x < 1