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Math Help - Inequality problem

  1. #1
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    Inequality problem

    The following problem raises some questions to me as to how the answer came to be:

    7(x+4) (greater than or equal) 6(x-3)+x

    After going through the problem I end up with an answer of:

    0 is (greater than or equal) to -46

    Not sure whats happening here because when I look up the answer I see it charted on the line from end to end going outward and an answer of

    (-infinity sign, infinity sign)
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  2. #2
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    Re: Inequality problem

    There are no solution for this equation since 46 can be equal to 0
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  3. #3
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    Re: Inequality problem

    Quote Originally Posted by itgl72 View Post
    The following problem raises some questions to me as to how the answer came to be:

    7(x+4) (greater than or equal) 6(x-3)+x

    After going through the problem I end up with an answer of:

    0 is (greater than or equal) to -46

    Not sure whats happening here because when I look up the answer I see it charted on the line from end to end going outward and an answer of

    (-infinity sign, infinity sign)
    \displaystyle \begin{align*} 7(x + 4) &\geq 6(x - 3) + x \\ 7x + 28 &\geq 6x - 18 + x \\ 7x + 28 &\geq 7x - 18 \\ 28 &\geq -18 \end{align*}

    This final statement is true no matter what the value of x, so the original inequality holds true for all x. So the solution is \displaystyle \begin{align*} x \in (-\infty, \infty) \end{align*}.
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