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solving equations with two absolute value brackets

|x+4| = |x-2|
so i want to know how to do this? do i always have to write out the four piecewise possibilities? that be ++ -+ and +-

x+4 = x-2
4 = -2 not solution

-(x+4) = x-2
-x-4 = x-2
-4 = 2x-2
-1 = x solution

x+4 = -(x-2)
x+4 = -x+2
2x+4 = 2
x = -1 solution

  • math-calculus oops -

    i forgot put the other one

    -(x+4) = -(x-2)
    -x+4 = -x+2
    4 = 2 no solution

  • math-calculus -

    you are correct.

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