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

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$\notin$ (6, -6) .

Apr 25, 2016

$a > 6 \mathmr{and} a < - 18$. -

#### Explanation:

$| a + 6 | > 6$ is the combined inequality for the pair $\pm \left(a + 6\right) > 12$..

#a+6 > 12 to a >6.

$- \left(a + 6\right) > 12 \to - a - 6 > 12 \mathmr{and} a < - 18$

So, a is outside the closed interval $\left[- 18 , 6\right]$..