`***` Lời giải chi tiết `***`
`a)`
`(2)/(3)x+4=-12`
`=>(2)/(3)x=-16`
`=>x=-16:(2)/(3)`
`=>x=-16.(3)/(2)`
`=>x=-24`
`b)`
`(3)/(4)+(1)/(4):x=-3`
`=>(1)/(4):x=-3-(3)/(4)`
`=>(1)/(4):x=-(15)/(4)`
`=>x=(1)/(4):(-(15)/(4))`
`=>x=-(1)/(15)`
`c)`
`|3x-5|=4`
`=>` \(\left[ \begin{array}{l}3x-5=4\\3x-5=-4\end{array} \right.\)
`=>` \(\left[ \begin{array}{l}3x=9\\3x=1\end{array} \right.\)
`=>` \(\left[ \begin{array}{l}x=3\\x=\dfrac{1}{3}\end{array} \right.\)
Vậy `x∈{3;(1)/(3)}`
`d)`
`(x+1)/(10)+(x+1)/(11)+(x+1)/(12)=(x+1)/(13)+(x+1)/(14)`
`=>(x+1)/(10)+(x+1)/(11)+(x+1)/(12)-(x+1)/(13)-(x+1)/(14)=0`
`=>(x+1)((1)/(10)+(1)/(11)+(1)/(12)-(1)/(13)-(1)/(14))=0`
`=>x+1=0` . Vì `(1)/(10)+(1)/(11)+(1)/(12)-(1)/(13)-(1)/(14)\ne0`
`=>x=-1`
`e***)`
`(x+4)/(2000)+(x+3)/(2001)=(x+2)/(2002)+(x+1)/(2003)`
`=>((x+4)/(2000)+1)+((x+3)/(2001)+1)=((x+2)/(2002)+1)+((x+1)/(2003)+1)`
`=>(x+2004)/(2000)+(x+2004)/(2001)=(x+2004)/(2002)+(x+2004)/(2003)`
`=>(x+2004)/(2000)+(x+2004)/(2001)-(x+2004)/(2002)-(x+2004)/(2003)=0`
`=>(x+2004)((1)/(2000)+(1)/(2001)-(1)/(2002)-(1)/(2003))=0`
`=>x+2004=0` . Vì `(1)/(2000)+(1)/(2001)-(1)/(2002)-(1)/(2003)\ne0`
`=>x=-2004`
