Can you please help me solve this equation and explain how you got the answer? Thank you! Solve Equation: |2x+3|=|x-6|?

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  • Bebe
    Lv 4
    5 years ago
    Favorite Answer

    |2x+3|=|x-6|

    As each term |a+b| has 2 scenarios (a+b) or –(a+b), 2 terms will have 4 possible scenarios:

    (a) Both positive

     2x+3 = x-6 → x = -9

    (b) LHS negative

     -(2x+3) = x-6 → x = 1

    (c) RHS negative

     2x+3 = -(x-6)  → x = 1

    (d) Both negative

     -(2x+3) = -(x-6)  → x = -9

    Since both (a) & (d) are the same mathematically, and (b) & (c) are the same, all you need is 2 scenarios:

    (i) make both sides the same sign ((a) or (d)), or

    (ii) change the sign of one side ((b) or (c)).

    GRAPH

    http://www.mathsisfun.com/data/function-grapher.ph...

    Enter the following to plot:

    y = abs(2x+3)

    y = abs(x-6)

    There will be 2 intersection points, where x=1 and x=-9.

    .

    • Danny5 years agoReport

      Thanks I understand how to get the -9 but how are you getting 1? If you could explain that part further I'd really appreciate it!

  • 5 years ago

    Obviously, if 2x + 3 = x - 6 (with no absolute value bars), then the absolute values would be equal too.

    So one answer comes from that equation.

    2x + 3 = x - 6

    -x - 3.. -x - 3

    --------------------

    x = -9

    However, if either part is the opposite of the other part, that would work too. So make one part be its opposite and solve that equation as well.

    either -(2x + 3) = x - 6

    -2x - 3 = x - 6

    or 2x + 3 = -(x - 6)

    2x + 3 = -x + 6

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