solve the inequality |2x - 3| <(equal to) 3

Answer 1

|2x-3| <= 3
(2x-3)^2 <= 9
4x^2-12x+9 <= 9
4x(x-3) <= 0
This is a parabola, which dips below the x-axis between the roots. So,
0 <= x <= 3

Or, you can solve two inequalities.
#1. for 2x-3 >= 0 (x >= 3/2),
2x-3 <= 3
2x <= 6
x <= 3

#2. for 2x-3 < 0 (x < 3/2),
-(2x-3) <= 3
2x-3 >= -3
x >= 0

so, 0 <= x <= 3

Answer 2

Thank you so much:)