Solve the equation.. absolute value of [x] = x/2 + 3?

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(I use the | x | notation for the absolute value of x)

Case 1 (x>=0):
x=x/2 + 3
2x=x+6
x=6 (which satisfies x>=0)

Case 2 (x<0):
-x=x/2 + 3
-2x=x+6
3x= -6
x= -2 (which satisfies x<0)

so x = -2, 6...Show more

If x>0 |x|=x so x=x/2+3 so x=?
If x<0 |x|=-x so -x=x/2+3 so x=?...Show more

x^2 - (x/2+3)^2=0
(x-x/2-3)(x+x/2+3)=0
X/2=3. So x= 6. Or 3x/2=-3. X=-2...Show more

|x| = x/2 + 3

let x<0
|x|=-x
hence
-x = x/2 + 3 => x₁=-2

let x>=0
|x|=x
hence
x = x/2 + 3 => x₂=6...Show more

Well multiply each side by 2 and get 2x= x + 3 then subtract the x from the 2x and get x=3...Show more