Question

How do you solve `3|x+11|=24`?

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 + 11))/color(red)(3) = 24/color(red)(3)`

`(color(red)(cancel(color(black)(3)))abs(x + 11))/cancel(color(red)(3)) = 8`

`abs(x + 11) = 8`

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 + 11 = -8`

`x + 11 - color(red)(11) = -8 - color(red)(11)`

`x + 0 = -19`

`x = -19`

Solution 2:

`x + 11 = 8`

`x + 11 - color(red)(11) = 8 - color(red)(11)`

`x + 0 = -3`

`x = -3`

The Solutions Are: `x = -19` and `x = -3`