Question

giải phương trình sau |x+1|=|2x+3|

Answer 1

`|x+1|=|2x+3|`
`<=>` $\left[ \begin{array}{l}x+1=2x+3\\x+1=-2x-3\end{array} \right.$
`<=>` $\left[ \begin{array}{l}x=-2\\3x=-4\end{array} \right.$
`<=>` $\left[ \begin{array}{l}x=-2\\x=-\dfrac43\end{array} \right.$
Vậy `S={-2,-4/3}`

Answer 2

 $| x + 1 | = | 2x + 3 |$

$<=>(| x + 1 |)^2 = (| 2x + 3 |)^2$`

$<=>x^2 + 2x + 1 = 4x^2 + 12x + 9$

$<=> 3x^2 + 10x + 8 = 0$

$<=>3x^2 + 6x + 4x + 8 = 0$

$<=> 3x ( x + 2 ) + 4 ( x + 2 ) = 0$

$<=> ( x + 2 ) ( 3x + 4 ) = 0 $

$<=>\left[\begin{array}{}x = -2\\x = \dfrac{-4}{3}\end{array} \right.$

Vậy $ S = { -2 ; \dfrac{-4}{3} }$