Algebra

The partners are given the literal inequality ax+b>c to solve for x. Joaquin says that he will solve it just like an equation. Serena says that he needs to be careful because if a is a negative number, the solution will be different. What do you say? What are the solutions for the inequality?

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  1. a x + b > c

    Subtract b to both sides

    a x + b - b > c - b

    a x > c - b

    If you multiply or divide both sides of an inequality by a negative number, reverse the direction of the inequality sign.


    So if a > 0 then:

    a x > c - b

    If a < 0 then:

    a x < c - b

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    posted by Bosnian
  2. Thank you, I appreciate the help!

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  3. a > 0

    x > ( c - b ) / a


    a < 0

    x < ( c - b ) / a

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    posted by Bosnian
  4. ax > c - b
    x > (c-b)/a

    let's set some values for a, b, c, and x
    of course our values have to satisfy the original
    eg. x = 3, a = 5 , c = 10, b = 8
    in original: 5(3) > 10-8 , true
    in my statement: 3 > 2/5 , true

    e.g. x = -5, a = 2, b = 20, c = 5
    in original: 2(-5) + 20 > 5 , true
    in mine: -5 > (5-20)/2 , -5 > -7.5 , true

    x=-5 , a= -2, b= -20 c = -5
    in original: -2(-5) - 20 > -5 , -10 > -5 , false
    in mine: -5 > (-5+20)/-2 , -5 > 7.5 , still false

    e.g. x = -5, a=2, b=20,c=-5
    original: 2(-5) + 20 > -5 , true
    mine: -5 > (-5-20)/2 , -5 > -7.5 , still true

    what do you think ?

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    posted by Reiny

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