# How do you solve and graph abs(9-x)>21?

$x < - 12 , x > 30$

#### Explanation:

Remember that the absolute value sign will always return a negative, so that, for instance where we have $\left\mid x \right\mid = 3$, $x$ can be 3 but it can also be $- 3$. And so we need to look at the positive and negative values that can be inside the absolute value sign.

Positive

$9 - x > 21$

$- x > 12$

$x < - 12$

Negative

$- \left(9 - x\right) > 21$

$- 9 + x > 21$

$x > 30$

Put it together and we have:

$x < - 12 , x > 30$

To graph this, place hollow circles around $- 12$ and 30 to indicate that they are not part of the solution. Then draw rays heading away from the origin (the ray from $- 12$ points towards larger negative values while the ray from 30 points towards larger positive values).