Question

1, |2x-5|=2-x

2, |3x-2|+x=11

3, |2x-1|=1-2x

4, |-4x|=x²+4

Answer 1

1. th1: 2x-5= 2-x nếu 2x-5>0 => x>\(\dfrac{5}{2}\)

2x-5=2-x

3x= 7

x=\(\dfrac{7}{3}\)(loại)

th2: 2x-5= -2-x nếu 2x-5 <0 => x<\(\dfrac{5}{2}\)

2x-5= -2-x

x= -1 (chọn)

S={-1}

2.|3x-2|+x=11

|3x-2| = 11-x

th1: 3x-2=11-x nếu 3x-2 >0 => x>\(\dfrac{2}{3}\)

3x-2= 11-x

4x= 13

x=\(\dfrac{13}{4}\)(chọn)

th2: 3x-2= -11-x nếu 3x-2<0 => x< \(\dfrac{2}{3}\)

3x-2=-11-x

4x= -9

x= \(\dfrac{-9}{4}\)(chọn)

S={\(\dfrac{13}{4}\); \(\dfrac{-9}{4}\)}

3. th1: 2x-1= 1-2x nếu 2x-1>0 => x>\(\dfrac{1}{2}\)

2x-1=1-2x

4x= 2

x=\(\dfrac{1}{2}\) (chọn)

th2: 2x-1=-1-2x nếu 2x-1<0 => x<\(\dfrac{1}{2}\)

2x-1=-1-2x

4x= 0

x= 0 (chọn)

S={\(\dfrac{1}{2}\); 0}