Question

How do you solve `|b | - 2< 89`?

Answer 1

First, add `2` to both sides: `|b| < 91`.

So, we know that `b` is less than `91` and greater than `-91`.

Thus, `b` < 91 and b > -91.

`(-91, 91)`

Answer 2

See a solution process below:

Explanation:

First, add `color(red)(2)` to each side of the inequality to isolate the absolute value function while keeping the inequality balanced:

`abs(b) - 2 + color(red)(2) < 89 + color(red)(2)`

`abs(b) - 0 < 91`

`abs(b) < 91`

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.

`-91 < b < 91`

Or

`b > -91` and `b < 91`

Or, in interval notation:

`(-91, 91)`