Question

a)2|x|-|x+3|-1=0

b)|x+1|-2|x-1|=x

c)|2x+3|-|x|+x-1=0

Answer 1

a: TH1: x<-3

=>-2x-(-x-3)-1=0

=>-2x-1+x+3=0

=>-x+2=0

=>x=2(loại)

TH2: -3<=x<0

=>-2x-x-3-1=0

=>-3x-4=0

=>x=-4/3(nhận)

TH3: x>=0

=>2x-x-3-1=0

=>x-4=0

=>x=4

b: TH1: x<-1

=>-x-1-2(1-x)=x

=>-x-1-2+2x=x

=>x-3=x(loại)

TH2: -1<=x<1

=>x+1-2(1-x)=x

=>1-2(1-x)=0

=>2(1-x)=1

=>1-x=1/2

=>x=1/2(nhận)

TH3: x>=1

=>x+1-2x+2=x

=>-x+3-x=0

=>3-2x=0

=>x=3/2(nhận)

c: TH1: x<-3/2

=>-2x-3+x+x-1=0

=>-4=0(loại)

TH2: -3/2<=x<0

=>2x+3+x+x-1=0

=>4x+2=0

=>x=-1/2(nhận)

TH3: x>=0

=>2x+3-x+x-1=0

=>2x+2=0

=>x=-1(loại)