Question

How do you solve `|r + 3| ≥ 7`?

Answer 1

See a solution process below:

Explanation:

The absolute value function takes any 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.

`-7 >= r + 3 >= 7`

Now, subtract `color(red)(3)` from each side of the system of inequalities to solve for `r` while keeping the equation balanced:

`-7 - color(red)(3) >= r + 3 - color(red)(3) >= 7 - color(red)(3)`

`-10 >= r + 0 >= 4`

`-10 >= r >= 4`

Or

`r <= -10`; `r >= 4`

Or, in interval notation:

`(-oo, -10]`; `[4, +oo)`