How do you solve # |a+6|>12#?

2 Answers
SCooke
Apr 25, 2016

Solve it as a normal equation, then examine the 'inequality' boundaries.

Explanation:

In general, a one-sided inequality can be solved by first solving the equality, as that will give you the “boundary” of the solution. In this case |a+6|=12. ONLY the 'a' varies, so we can remove the 6 from the inequality by normal subtraction. |a| = 12 – 6 = 6.

So now we know that our 'boundary' is when a = 6 and when a = -6. Anything between those boundaries will not satisfy the inequality (the resulting values will be between 0 and 11), so our inequality solution is |a| > 6 . This may also be written as a#!in# (6, -6) .

A. S. Adikesavan
Apr 25, 2016

#a>6 and a<-18#. -

Explanation:

#|a+6|>6# is the combined inequality for the pair #+-(a+6)>12#..

#a+6 > 12 to a >6.

#-(a+6)>12 to -a-6>12 or a < -18#

So, a is outside the closed interval # [-18, 6]#..

Related questions
See all questions in Absolute Value Inequalities
Impact of this question
1881 views around the world
You can reuse this answer
Creative Commons License