Đáp án:
$\\$
`|x + 1| + |x+3|` `(1)`
Có : \(\left\{ \begin{array}{l}|x+1|=0\\|x+3|=0\end{array} \right.\) `↔` \(\left\{ \begin{array}{l}x+1=0\\x+3=0\end{array} \right.\) `↔` \(\left\{ \begin{array}{l}x=0-1\\x=0-3\end{array} \right.\) `↔` \(\left\{ \begin{array}{l}x=-1\\x=-3\end{array} \right.\)
Ta có bảng xét dấu :
$\begin{array}{|c|c|c|c|c|c|c|}\hline x& & -1 & & -3 & \\\hline x+1& - & 0 & + & | &+ \\\hline x + 3&-&|&-&0&+\\\hline\end{array}$
$\bullet$ Khi `x < -1` thì `(1)` có dạng :
`- (x+1) - (x+3)`
`= -x - 1 - x - 3`
`= (-x-x) + (-1-3)`
`= -2x - 4`
$\bullet$ Khi $-1 \leqslant x \leqslant -3$ thì `(1)` có dạng :
`(x + 1) - (x + 3)`
`= x + 1 - x - 3`
`= (x-x) + (1-3)`
`= -2`
$\bullet$ Khi `x > -3` thì `(1)` có dạng :
`(x + 1) + (x + 3)`
`= x + 1 +x + 3`
`= (x+x) + (1+3)`
`=2x+4`
