Question

How do you solve `abs(x-3)>=1`?

Answer 1

`2 geq x geq 4`

Explanation:

From `|x-3| geq 1` it follows that `x-3 leq -1` and `x-3 geq 1`

Adding 3 to both sides of the equations we get
`x leq 2` and `x geq 4` which are our two solutions.

Also, looking at the graph of `y=|x-3|` we can see which values of y are greater than or equal to `1` and these are indeed the values where x is less than or equal to 2, and where x is greater than or equal to 4.

graph{|x-3| [-10, 10, -5, 5]}