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|2x-3|-|2x+5| = 0 i please need helps with this.

  • math-calculus -

    if 2x-3 >= 0 then you have
    2x-3 - |2x-5| = 0
    Now, if 2x-5 >= 0, that gives
    2x-3 - (2x-5) = 0
    2 = 0
    no good

    If 2x-5 < 0 you have

    2x-3 - -(2x-5) = 0
    2x-3 + 2x-5 = 0
    4x - 8 = 0
    x = 2
    since x=2 satisfies both conditions
    2x-56 < 0 and 2x-3 >= 0, it's a solution.

    Work through the other possibilities to find that x=2 is the only solution.

    Makes sense, since the graphs of the two absolute values are v-shaped with equal slopes, so they intersect in only one point.

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