Question

How do you solve `|x - 13| + 10\leq 3`?

Answer 1

See a solution process below:

Explanation:

First, subtract `color(red)(10)` from each side of the inequality to isolate the absolute value term:

`abs(x - 13) + 10 - color(red)(10) <= 3 - color(red)(10)`

`abs(x - 13) + 0 <= -7`

`abs(x - 13) <= -7`

The absolute value function takes any term and transforms it to its non-negative form. Therefore, output of the absolute value function will always be greater than or equal to `0` and cannot be less than `0`.

Therefore, there are no solutions to this inequality because `-7` is less than `0`.

Or, the solution is the null or empty set: `{O/}`