Question

How do you solve the equation `abs(ax)=b`?

Answer 1

Assuming the solution being requested is for `x`, see a solution process below:

Explanation:

The absolute value function takes any negative or positive 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

`ax = -b`

`(ax)/color(red)(a) = -b/color(red)(a)`

`(color(red)(cancel(color(black)(a)))x)/cancel(color(red)(a)) = -b/a`

`x = -b/a`

Solution 2

`ax = b`

`(ax)/color(red)(a) = b/color(red)(a)`

`(color(red)(cancel(color(black)(a)))x)/cancel(color(red)(a)) = b/a`

`x = b/a`

The Solutions Are: `x = -b/a` and `x = b/a`