Đáp án : `x=3` Giải thích các bước giải : `|x+1|+|x+2|=3x` Vì `|x+1| ≥ 0; |x+2| ≥ 0` `=>|x+1|+|x+2| ≥ 0` `=>3x ≥ 0` `=>x ≥ 0` `+)x ≥ 0 => |x+1| > 0 => |x+1|=x+1` `+)x ≥ 0 => |x+2| > 0 => |x+2|=x+2` `+)|x+1|+|x+2|=3x` `<=>x+1+x+2=3x` `<=>2x+3=3x` `<=>2x-3x=-3` `<=>-x=-3` `<=>x=3` Vậy `x=3` Bình luận
\(|x+1|+|x+2|=3x \,\,(ĐK : 3x\geq0) \\ \Leftrightarrow \left[ \begin{array}{l}(x+1)+(x+2)=3x\\-(x+1)-(x+2)=3x\end{array} \right. \\ \Leftrightarrow \left[ \begin{array}{l}x+1+x+2=3x\\-x-1-x-2=3x \end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}x+x-3x=-1-2\\-x-x-3x=1+2\end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}-x=-3\\-5x=3\end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}x=3\,\,(TM)\\x=\dfrac{-5}{3}\,\,\text{(loại do}\,\,3x=-5<0)\end{array} \right. \\ \text{Vậy}\,\,x=3\) Bình luận
Đáp án :
`x=3`
Giải thích các bước giải :
`|x+1|+|x+2|=3x`
Vì `|x+1| ≥ 0; |x+2| ≥ 0`
`=>|x+1|+|x+2| ≥ 0`
`=>3x ≥ 0`
`=>x ≥ 0`
`+)x ≥ 0 => |x+1| > 0 => |x+1|=x+1`
`+)x ≥ 0 => |x+2| > 0 => |x+2|=x+2`
`+)|x+1|+|x+2|=3x`
`<=>x+1+x+2=3x`
`<=>2x+3=3x`
`<=>2x-3x=-3`
`<=>-x=-3`
`<=>x=3`
Vậy `x=3`
\(|x+1|+|x+2|=3x \,\,(ĐK : 3x\geq0) \\ \Leftrightarrow \left[ \begin{array}{l}(x+1)+(x+2)=3x\\-(x+1)-(x+2)=3x\end{array} \right. \\ \Leftrightarrow \left[ \begin{array}{l}x+1+x+2=3x\\-x-1-x-2=3x \end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}x+x-3x=-1-2\\-x-x-3x=1+2\end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}-x=-3\\-5x=3\end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}x=3\,\,(TM)\\x=\dfrac{-5}{3}\,\,\text{(loại do}\,\,3x=-5<0)\end{array} \right. \\ \text{Vậy}\,\,x=3\)