Question

How do you solve and graph `abs(x-2)<=3`?

Answer 1

See a solution process below:

Explanation:

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

`-3 <= x - 2 <= 3`

Now, add `color(red)(2)` to each segment of the system of inequalities to solve for `x` while keeping the equation balanced:

`-3 + color(red)(2) <= x - 2 + color(red)(2) <= 3 + color(red)(2)`

`-1 <= x - 0 <= 5`

`-1 <= x <= 5`

The solution is:

`x >= -1` and `x <= 5`

Or, in interval notation form:

`[-1, 5]`