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Math Help - Absolutely Annoying (Absolute value)

  1. #1
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    Absolutely Annoying (Absolute value)

    Hi MHF, stuck on a homework problem. I need to solve for a.

    |2a+8|=|2a-6|
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  2. #2
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    |a|= |b| reduces to two equations: a= b or a= -b.

    |2a+ 8|= |2a- 6| reduces to 2a+ 8= 2a- 6 or 2a+ 8= -(2a- 6). Can you solve those (one of them has no solution).
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  3. #3
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    Sketch these functions, you will see there is no solution.
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  4. #4
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    Quote Originally Posted by HallsofIvy View Post
    |a|= |b| reduces to two equations: a= b or a= -b.

    |2a+ 8|= |2a- 6| reduces to 2a+ 8= 2a- 6 or 2a+ 8= -(2a- 6). Can you solve those (one of them has no solution).
    So, I'm guessing 2a+8=2a-6 would have no solution. 2a+8=-2a+6 would come out to a=-1/2

    Correct?

    I was on the right track, just wasn't sure of myself.
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  5. #5
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    yes you are correct
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  6. #6
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    Quote Originally Posted by pickslides View Post
    Sketch these functions, you will see there is no solution.
    How is a= -1/2 not a solution?
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  7. #7
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    Quote Originally Posted by Fails_at_Math View Post
    So, I'm guessing 2a+8=2a-6 would have no solution. 2a+8=-2a+6 would come out to a=-1/2

    Correct?

    I was on the right track, just wasn't sure of myself.
    Don't guess! If 2a+ 8= -2a+ 6, adding 2a to both sides gives 8= 6 which is NOT true. There is no value of a which makes it true. Yes, if a= -1/2,
    then 2a+ 8= 2(-1/2)+ 8= -1+ 8= 7 and |7|= 7, while 2a- 6= 2(-1/2)- 6= -1- 6= -7 and |-7|= 7.
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  8. #8
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    Quote Originally Posted by Fails_at_Math View Post

    |2a+8|=|2a-6|
    Both sides positives, so you can square them and then 32a+64=-24a+36, and it follows that a=-\frac12.
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