Answer:
There are no solutions to the inequality.
Step-by-step explanation:
|x - 3| < x – 3
1. Separate the inequality into two separate ones.
(1) x – 3 < x – 3
(2) x – 3 < -(x – 3)
2. Solve each equation separately
(a) Equation (1)
[tex]\begin{array}{rcl}x - 3 & < & x - 3\\x & < & x\\\end{array}\\\text{This is impossible. No solutions exist.}[/tex]
(b) Equation (2)
[tex]\begin{array}{rcl}x - 3 & < & -(x - 3)\\x - 3 & < & -x + 3\\x & <& -x + 6\\2x & < & 6\\x & < & 3\\\end{array}\\\text{This is impossible. No solutions exist}[/tex]
For example, if x = 0, we get
|0 - 3| < 0 - 3 or
3 < -3
