Simplify to an answer of the form ax b or ax b for x in 4

Simplify to an answer of the form ax + b or ax - b for x in [4, 6]. |x - 2| - 3|x - 7| = _____

Solution

given x is in interval [4,6]

so x-2 >0 , x-7 <0

when a>0 ,|a|=a

when a<0 ,|a|=-a

now

|x-2|-3|x-7|

=(x-2) -3(-(x-7))

=(x-2) -3(-x+7)

=x-2 +3x-21

=4x-23