Đáp án:
`a)|x-1|=3x+2(x>=-2/3)`
`+)x-1=3x+2`
`<=>2x=-3`
`<=>x=-3/2(KTM)`
`+)x-1=-3x-2`
`<=>4x=-1`
`<=>x=-1/4(TM)`
`b)|3x-1|+2=x`
`<=>|3x-1|=x-2(x>=2)`
`+)3x-1=x-2`
`<=>2x=-1`
`<=>x=-1/2(KTM)`
`+)3x-1=2-x`
`<=>4x=3`
`<=>x=3/4(KTM)`
`|x+7|-x=7`
`<=>|x+7|=x+7`
Sử dụng tính chất:`|P|=P<=>P>=0`
`=>|x+7|=x+7`
`<=>x+7>=0`
`<=>x>=-7`
`d)|7-2x|+7=2x`
`<=>|7-2x|=2x-7`
`<=>|7-2x|=-(7-2x)`
Sử dụng tính chất `|P|=-P<=>P<=0`
`=>|7-2x|=-(7-2x)`
`<=>7-2x<=0`
`<=>7<=2x`
`<=>x>=7/2`
Bài 3:
`a)||2x-1|+1/2|=4/5`
Vì `|2x-1|>=0`
`=>|2x-1|+1/2>=1/2>0`
`=>||2x-1|+1/2|=|2x-1|+1/2`
`pt<=>|2x-1|+1/2=4/5`
`<=>|2x-1|=4/5-1/2=3/10`
`<=>` \(\left[ \begin{array}{l}2x-1=\dfrac{3}{10}\\2x-1=\dfrac{-3}{10}\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}2x=\dfrac{13}{10}\\2x=\dfrac{7}{10}\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x=\dfrac{13}{20}\\x=\dfrac{7}{20}\end{array} \right.\)
`b)|x^2+2|x-1/2||=x^2+2`
Tương tự như câu a ta có `|x^2+2|x-1/2||=x^2+2|x-1/2|`
`pt<=>x^2+2|x-1/2|=x^2+2`
`<=>2|x-1/2|=2`
`<=>|x-1/2|=1`
`<=>` \(\left[ \begin{array}{l}x-\dfrac12=1\\x-\dfrac12=-1\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x=\dfrac32\\x=-\dfrac12\end{array} \right.\)
