Answer: x=-2/3 x=-4
Step-by-step explanation:
[tex]|x-1|=|2x+3|\\[/tex]
Equate the submodular functions to zero:
x-1=0
x-1+1=0+1
x=1
2x+3=0
2x+3-3=0-3
2x=-3
Divide both parts of the equation by 2:
x=-1.5
Thus,
-∞____-1.5_____1____+∞
x∈[1,+∞)
x-1=2x+3
x-1-x-3=2x+3-x-3
-4=x∉[1,+∞)
x∈(-1.5,1)
-(x-1)=2x+3
-x+1=2x+3
-x+1+x-3=2x+3-x-3
-2=3x
Divide both parts of the equation by 3:
x=-2/3∈(-1.5,1)
x∈(-∞,-1.5]
-(x-1)=-(2x+3)
-x+1=-2x-3
-x+1+2x-1=-2x-3+2x-1
x=-4∈(-∞,-1.5]
