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Math Help - Absolute Value Equations

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    Absolute Value Equations

    How, when you are given an absolute value equation, solve it graphically on a real-number line?
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    Re: Absolute Value Equations

    Quote Originally Posted by Bashyboy View Post
    How, when you are given an absolute value equation, solve it graphically on a real-number line?
    You should know that the absolute value corresponds to the "size" of a number...

    So say |x| = 3. That means that the size of the number is 3 units from 0. Therefore x = -3 or x = 3. Does that make sense?
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    Re: Absolute Value Equations

    Yes, it does. But I become a bit more confounded with a problem like |x - 3| = 5. How would I solve one like this on a real number-line?
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    Re: Absolute Value Equations

    Quote Originally Posted by Bashyboy View Post
    Yes, it does. But I become a bit more confounded with a problem like |x - 3| = 5. How would I solve one like this on a real number-line?
    Well that means that the size of x - 3 is 5 units from 0.

    So \displaystyle x - 3 = -5 \implies x = -2 or \displaystyle x - 3 = 5 \implies x = 8.
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    Re: Absolute Value Equations

    I have another problem. I am given a real number line with the two points -3 an 1 marked on it. How do I write an absolute value equations from this data?
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    Re: Absolute Value Equations

    Quote Originally Posted by Bashyboy View Post
    I have another problem. I am given a real number line with the two points -3 an 1 marked on it. How do I write an absolute value equations from this data?
    If a<b then the equation \left| {x - \frac{{b + a}}{2}} \right| = \frac{{b - a}}{2} has solutions x=a\text{ or }x=b.
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    Re: Absolute Value Equations

    I am truly sorry, but I don't quite follow. I have not seen anything like this before.
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    Re: Absolute Value Equations

    Quote Originally Posted by Bashyboy View Post
    I am truly sorry, but I don't quite follow. I have not seen anything like this before.
    Are you saying that you cannot substitute a=-3~\&~b=1 into that?
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    Re: Absolute Value Equations

    No, plugging and chugging is quite simple. But I have never seen that formula you have presented me with. Also, the way the book wants me to solve it is just graphically.
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