a) |2x-1|=x+3
Nếu x\(\ge\)\(\dfrac{1}{2}\) thì: 2x-1=x+3
\(\Leftrightarrow\)x=4 (t/m)
Nếu x<\(\dfrac{1}{2}\) thì: 2x-1=-x-3
\(\Leftrightarrow\)x=\(\dfrac{-2}{3}\) (t/m)
b) |x+2|=|3x-1|
\(\Leftrightarrow\) (x+2)2=(3x-1)2\(\Leftrightarrow\)x2+4x+4=9x2-6x+1
\(\Leftrightarrow\)-8x2+10x+3=0\(\Leftrightarrow\)-8x2-2x+12x+3=0
\(\Leftrightarrow\)(4x+1)(-2x+3)=0\(\Leftrightarrow\)x\(\in\){\(\dfrac{-1}{4}\);\(\dfrac{3}{2}\)}
c)|x+1|+|x-2|=4
Lập bảng:
x | -1 2
x+1| -x-1 0 x+1 | x+1
x-2 | -x+2 | -x+2 0 x-2
VT | -2x+1 | 3 | 2x-1
Nếu x<-1 thì -2x+1=4\(\Leftrightarrow\)x=\(\dfrac{-3}{2}\) (t/m)
Nếu -1\(\le\)x<2 thì không có giá trị nào của x
Nếu 2\(\le\)x thì 2x-1=4\(\Leftrightarrow\)x=\(\dfrac{5}{2}\) (t/m)
Vậy x\(\in\){\(\dfrac{-3}{2};\dfrac{5}{2}\)}