Question

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

Answer 1

See a solution process below:

Explanation:

The absolute value function takes any negative or positive term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

`-1 >= x - 3 >= 1`

Add `color(red)(3)` to each segment of the system of inequalities to solve for `x` while keeping the system balanced:

`-1 + color(red)(3) >= x - 3 + color(red)(3) >= 1 + color(red)(3)`

`2 >= x - 0 >= 4`

`2 >= x >= 4`

Or

`x <= 2` and `x >= 4`

Or, in interval notation:

`(-oo, 2]` and `[4, +oo)`