a: A=|3x+3|+|3-2x|+x-1
=|3x+3|+|2x-3|+x-1
TH1: x<-1
=>A=-3x-3+3-2x+x-1
=(-3x-2x+x)+(-3+3-1)
=-4x-1
TH2: -1<=x<3/2
=>A=3x+3+(3-2x)+x-1
=4x+2+3-2x
=2x+5
TH3: x>=3/2
=>A=3x+3+2x-3+x-1
=6x-1
b: B=x-3-|2x+4|+|1-3x|
=x-3-|2x+4|+|3x-1|
TH1: \(x< -2\)
=>\(B=x-3-\left(-2x-4\right)+\left(1-3x\right)\)
=x-3+2x+4+1-3x
=(x+2x-3x)+(-3+4+1)
=1+1
=2
TH2: -2<=x<1/3
=>\(B=x-3-\left(2x+4\right)+\left(1-3x\right)\)
=x-3-2x-4+1-3x
=x-2x-3x-3-4+1
=-4x-6
TH3: x>=1/3
=>\(B=x-3-\left(2x+4\right)+\left(3x-1\right)\)
=x-3-2x-4+3x-1
=2x-8
c: C=|4-2x|+5x-3+|3x+2|
=|2x-4|+|3x+2|+5x-3
TH1: x<-2/3
=>\(C=4-2x-3x-2+5x-3\)
=4-2-3
=4-5
=-1
TH2: -2/3<=x<2
=>\(C=4-2x+3x+2+5x-3=6x+3\)
TH3: x>=2
=>C=2x-4+3x+2+5x-3
=10x+(-4+2-3)
=10x-5
d: D=|x+5|-4x+2-|2-3x|
=|x+5|-|3x-2|-4x+2
TH1: \(x< -5\)
=>\(D=-x-5-\left(2-3x\right)-4x+2\)
=-5x-3-2+3x
=-8x-5
TH2: -5<=x<2/3
=>\(D=x+5-\left(2-3x\right)-4x+2\)
=-3x+7-2+3x
=5
TH3: x>=2/3
=>\(D=x+5-\left(3x-2\right)-4x+2\)
=-3x+7-3x+2
=-6x+9
