Question

How do I solve |x+1|=|x-2|

Answer 1

|x+1|=|x-2|
±(x+1) = ±(x-2)

but +(x+1) = +(x-2) is the same as -(x+1) = -(x-2), so let's just solve
x+1 = x-2
1 = -2, which is highly unlikely, so this case has no solution

similarely, +(x+1) = -(x-2) is the same as -(x+1) = +(x-2), so solve
x + 1 = -x + 2
2x = 1
x = 1/2 is our only solution.

check by graphing:
y = |x+1| and y = |x-2|

Answer 2

or, try
(x+1)^2 = (x-2)^2
6x = 3
x = 1/2

Answer 3

Thank you.