Question

How do you solve `abs(x-16)<10`?

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.

`-10 < x - 16 < 10`

First, add `color(red)(16)` to each segment of the system of inequalities to solve for `x` while keeping the system balanced:

`-10 + color(red)(16) < x - 16 + color(red)(16) < 10 + color(red)(16)`

`6 < x - 0 < 26`

`6 < x < 26`

Or

`x > 6` and `x < 26`

Or, in interval notation

`(6, 26)`