Question

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

Answer 1

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) .

Answer 2

`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]`..