Question

| x-3 | < x-3

can someone give a step by step process on how to do this?

Answer 1

There are no solutions to the inequality.

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)

`\begin{array}{rcl}x - 3 & < & x - 3\\x & < & x\\\end{array}\\\text{This is impossible. No solutions exist.}`

(b) Equation (2)

`\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}`

For example, if x = 0, we get

|0 - 3| < 0 - 3 or

3 < -3