Multi-Step Inequalities

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Multi-Step Inequalities
5:38 — by Khan Academy

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Key Questions

  • There isn't that big of a difference between solving a multi-step equation and a multi-step inequality.

    When given the inequality solve as if your solving an equation but at the end there is a less than, greater than, or less than or greater than or equal to sign. One main difference is you switch the symbol when dividing by a negative.

  • I would start with arranging terms so that all variables are on one side.


    I hope that this was helpful.

  • Solve it like a normal equation, with a few rules however.

    #5x-4>21#

    #5x-4>21# (Add four to each side)

    #5x>25# (Divide by 5)

    #x>5#

    If you have to multiply or divide by a negative, the sign flips.

    #-5x-4>21# (Repeat the same steps)

    #-5x>25# Here we have to divide by a negative, -5, so the sign flips.

    #x<-5#

  • If your variable cancels out, there are two possible outcomes. Assuming you have an equation like

    #x+3=x+9->3=9#

    and the #x# variable cancels out. In this case, 3 is not equal to 9 so there is no solution.
    An example of the other case is

    #2x+12=2x+(3^2+3)->12=9+3=12#

    Because this statement it true, that means any number could be in the place of that variable.

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