Question

|x-1|=3x+2

Answer 1

TH1: x-1>=0 <=> x>=1 (dk : x>=1)

khi đó phương trình là:

x-1=3x+2

<=> x-3x =2+1

<=>-2x=3

<=>x=-3/2 (loại)

TH2: x-1<0 <=> x<1 (dk : x<1)

-(x-1)=3x+2

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

<=>-x-3x=2-1

<=>-4x=1

<=>x=-1/4 ( nhan )

vậy pt có tập nghiệm là S={-1/4}

Answer 2

TH1: \(x-1\ge0\Leftrightarrow x\ge1\)

pt \(\Rightarrow x-1=3x+2\)

\(\Leftrightarrow-2x=3\)

\(\Leftrightarrow x=-1,5\left(loai\right)\)

TH2: \(x-1< 0\Leftrightarrow x< 1\)

pt \(\Rightarrow1-x=3x+2\)

\(\Leftrightarrow-4x=1\)

\(\Leftrightarrow x=-0,25\)

Vậy \(S=\left\{-0,25\right\}\)

Answer 3

Cach khac

Dk : 3x+2 >= 0 <=> x >= -2/3

|x-1| = 3x + 2 <=> x-1 = 3x+2 hoac x-1=-3x-2

<=> x-3x=2+1 hoac x+3x = -2 + 1

<=> -2x = 3 hoac 4x = -1

<=> x = -3/2 ( loai ) hoac x = -1/4 ( nhan )

S = { -1/4 }

nhanh hon nhieu