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

1 Answer
Mar 27, 2018

Answer:

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)#