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Is This Considered a Linear Equation?

  1. Oct 27, 2014 #1
    I know that linear equations have variables, which have a power no greater than one.

    So, for example, 5x + 2 = 15 is linear, because the x is to the first power only.

    But what about this equation:
    x/x+2 = 80

    This has an x in the denominator. Could we consider this linear still, because no x/variable is to a power greater than 1? Thanks!
  2. jcsd
  3. Oct 27, 2014 #2


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    Homework Helper

    Is that supposed to be x/(x+2) = 80? Because what you wrote would be interpreted as

    [tex]\frac{x}{x}+2=80[/tex] which is not a true statement.

    If it's the former, then no, it's not linear.

    [tex]y=\frac{x}{x+2}[/tex] is what you'd call a rational function because it is comprised of a (linear) polynomial in the numerator and denominator.
  4. Oct 28, 2014 #3


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    As it is written, [tex]\frac{x}{x+ 2}= 80[/tex] it is not linear. But it can easily be converted to a linear equation:
    x= 80(x+ 2)= 80x+ 160. Some texts call that an "equation of linear type" rather than a "linear equation".
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