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Thread: Help inequalities

  1. #1
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    Help inequalities

    I'm having problems solving this two. Please help

    7x-5<4

    4/x -4>5
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  2. #2
    Super Member

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    Hello, Jerry!

    The general rule for solving inequalities is something like:

    . . Solve as if it were an equation except: when multiplying or
    . . . . dividing by a negative quantity, reverse the inequality.


    $\displaystyle 7x - 5\:\leq \:4$

    We are given: .. . $\displaystyle 7x - 5 \;\leq \;4$

    Add 5 to both sides: . $\displaystyle 7x\;\leq\;9$

    Divide by 7:. . . . . . . .$\displaystyle \boxed{x \;\leq \;\frac{9}{7}}$



    $\displaystyle \frac{4}{x} -4\:\geq\:5$

    There is one more rule:

    . . When taking reciprocals of both sides of an inequality,
    . . . . reverse the inequality.

    For example: .$\displaystyle 2 < 4\quad\Rightarrow\quad \frac{1}{2} > \frac{1}{4}$


    We are given: . . . $\displaystyle \frac{4}{x} - 4 \;\geq \;5$

    Add 4 to both sides: . $\displaystyle \frac{4}{x}\;\geq\;9$

    Take reciprocals: . . . $\displaystyle \frac{x}{4} \;\leq \;\frac{1}{9}$ .
    (reverse the sign)

    Multiply by 4: . . . . . .$\displaystyle \boxed{x\;\leq\;\frac{4}{9}}$

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