Question

How do you solve the equation `abs(x+a)=b`?

Answer 1

See a solution process below:

Explanation:

Assuming solving the equation for `x`:

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.

Solution 1:

`x + a = -b`

`x + a - color(red)(a) = -b - color(red)(a)`

`x + 0 = -b - a`

`x = -b - a`

Solution 2:

`x + a = b`

`x + a - color(red)(a) = b - color(red)(a)`

`x + 0 = b - a`

`x = b - a`

The Solutions Are:

`x = -b - a` and `x = b - a`

Or

`x = +-b - a`