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Math Help - Linear Equation: Removing Negative Variables

  1. #1
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    Linear Equation: Removing Negative Variables

    Problem:
    4x-2>5x+1

    -x>3

    x<-3

    In the final step the negative variable was removed. In the book, no additional steps or explanation is given. I am assuming the correct procedure when you have a negative variable is to multiply both sides of the equation by -1.

    therefore

    (-x)(-1) > (3)(-1)

    and in addition since we multiplied by a negative quantity within an inequality we flip the sign to
    x<-3

    Is this correct?
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  2. #2
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    Re: Linear Equation: Removing Negative Variables

    Quote Originally Posted by allyourbass2212 View Post
    Problem:
    4x-2>5x+1

    -x>3

    x<-3

    In the final step the negative variable was removed. In the book, no additional steps or explanation is given. I am assuming the correct procedure when you have a negative variable is to multiply both sides of the equation by -1.

    therefore

    (-x)(-1) > (3)(-1)

    and in addition since we multiplied by a negative quantity within an inequality we flip the sign to
    x<-3

    Is this correct? <--- yes
    In addition: You have to flip the sign when calculating the reciprocal:

    Example: .............. 3 < 5~\implies~\frac13 > \frac15
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