Question

|x-1| = |2x+3| ; solve for x

Answer 1

Answer: x=-2/3 x=-4

Explanation:

`|x-1|=|2x+3|\\`

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]