\(\left|x+1\right|+2x=-2\)
\(\Rightarrow\left|x+1\right|=-2-2x\)
\(\Rightarrow x+1=\pm\left(-2-2x\right)\)
+) \(x+1=-2-2x\)
\(\Rightarrow x+2x=-2-1\)
\(\Rightarrow3x=-3\)
\(\Rightarrow x=-1\)
+) \(x+1=-\left(-2-2x\right)\)
\(x+1=2+2x\)
\(\Rightarrow x-2x=2-1\)
\(\Rightarrow-x=1\)
\(\Rightarrow x=-1\)
Vậy \(x=-1\)
\(\)
|x + 1| + 2x = -2
+ Với x < -1 thì |x + 1| = -(x + 1) = -x - 1
Ta có: -x - 1 + 2x = -2
=> x - 1 = -2
=> x = -2 + 1
=> x = -1, thỏa mãn x < -1
+ Với \(x\ge-1\) thì |x + 1| = x + 1
Ta có: x + 1 + 2x = -2
=> 3x = -2 - 1
=> 3x = -3
=> x = -3 : 3
=> x = -1, thỏa mãn \(x\ge-1\)
Vậy x = -1
