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Thread: Graphing Absolute Value Inequality: 9|x - 2| - 10 >= -64

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    Graphing Absolute Value Inequality: 9|x - 2| - 10 >= -64

    I have a question. What's the answer to 9|x-2|-10>=-64? I thought it was all real numbers, but my teacher said it was no solution since absolute value can't equal a negative. Thanks in advance.

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    Elite Member mmm4444bot's Avatar
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    Quote Originally Posted by jennie View Post
    What's the [solution for] 9|x-2| - 10 >= -64 ?

    I thought it was all real numbers, but my teacher said it was no solution since absolute value can't equal a negative.
    I agree with your solution; your teacher might have been thinking about a different situation.

    The inequality symbol ≥ means greater than OR equal.

    As long as the left-hand side evaluates to a number that is greater than -64, the inequality is true. This happens for any value of x.

    If you solved the inequality by hand, you ought to have reached this:

    |x - 2| ≥ -6

    This shows that x can be any Real number because |x-2| is non-negative, and any non-negative number is greater than -6.
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

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    Elite Member mmm4444bot's Avatar
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    Graphing each side of the given inequality is another way to solve it.

    The graph of the left-hand side (green) lies entirely above the graph of the right-hand side (red).

    In other words, at each value of x, the value of y on the green graph is greater than the value of y on the red graph.
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    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

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