Question

How do you solve `3|x + 4| = - 9`?

Answer 1

See a solution process below:

Explanation:

First, divide each side of the equation by `color(red)(3)` to isolate the absolute value function while keeping the equation balanced:

`(3abs(x + 4))/color(red)(3) = -9/color(red)(3)`

`(color(red)(cancel(color(black)(3)))abs(x + 4))/cancel(color(red)(3)) = -3`

`abs(x + 4)= -3`

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.

Because the absolute value function cannot generate a negative number there is no solution to this problem.

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