Question

How do you solve the inequality `abs(x + 2) <=11`?

Answer 1

Determine your boundary conditions to solve for the minimum and maximum values of x, then write out the final inequality `-13lexle9`

Explanation:

We need to determine the boundaries where this inequality is true. Because we're dealing with an absolute value, the two scenarios look like this:

`x+2le11`

`x+2ge-11`

Notice I flipped the sign for the opposite boundary. This is because we're dealing with the negative solution, and when you flip a sign on an inequality, the direction of the comparator flips as well.

Now, let's solve for x in both expressions:

`x+2le11`

`xcancel(+2-2)le11-2`

`color(red)(xle9)`

`x+2ge-11`

`xcancel(+2-2)ge-11-2`

`color(blue)(xge-13)`

Now that we know our bounds, we can write it as a single inequality:

`color(green)(-13lexle9)`