# Math Help - Answer to the form ax + b

1. ## Answer to the form ax + b

Simplify to an answer in the form of ax + b for x in [3,5].
$
|x-2| - 4 |x-6|
$

2. For all $x \in [3, 5], x - 2$ is positive and $x - 6$ is negative.

Thus, for all $x \in [3, 5], |x - 2| = x - 2$ and $|x - 6| = 6 - x$.

3. Originally Posted by BadMaterial
Simplify to an answer in the form of ax + b for x in [3,5].
$
|x-2| - 4 |x-6|
$
|x-2| = (x-2) because (x-2)>0 for $x\in[3,5]$.

|x-6| = -(x-6) because (x-6)<0 for $x\in[3,5]$.

Use these properties:

$|x-2| - 4 |x-6| = (x-2)-4(-(x-6))$

I'll leave the rest for you.