How do you solve the inequality #abs(x + 2) <=11#?
Determine your boundary conditions to solve for the minimum and maximum values of x, then write out the final inequality
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:
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:
Now that we know our bounds, we can write it as a single inequality: