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Thread: Foreign Household Voltage

  1. #1
    Super Member harpazo's Avatar
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    Foreign Household Voltage

    In other countries, normal household voltage is 220 volts. It is acceptable for the actual voltage x to differ from normal by at most 8 volts. A formula that describes this is |x - 220| ≤ 8.

    A. Show that a voltage of 214 is acceptable.

    B. Show that a voltage of 209 is not acceptable.

    Question:

    Must I replace x with 214 and then 209 respectively for parts A and B?

    Why is the ≤ applied to AT MOST inequalities and GREATER THAN OR EQUAL TO applied to AT LEAST inequalities?
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    Re: Foreign Household Voltage

    Quote Originally Posted by harpazo View Post
    Question:
    Why is the ≤ applied to AT MOST inequalities and GREATER THAN OR EQUAL TO applied to AT LEAST inequalities?
    Prof Halls has said this but now you learn it.
    Absolute value is a metric, therefore it is not negative.
    $|x-a|$ is the measure of the distance from $x$ to $a$.
    $|x-5|$ is the measure of the distance from $x$ to $5$.
    $|x-3|<6$ says that $x$ is less than six units from $3$.
    $|x+8|>5$ says that $x$ is more than five units from $-8$.
    $|x+1|\le 7$ says that $x$ is at most than seven units from $-1$.
    $|x-4|\ge 7$ says that $x$ is at least seven units from $4$.
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    Re: Foreign Household Voltage

    $|x- 220|\le 8$ is the same as $-8\le x- 220\le 8$. Adding 220 to each part, $220- 8\le x \le 220+ 8$ or $212 \le x\le 228$.
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    Re: Foreign Household Voltage

    Quote Originally Posted by Plato View Post
    Prof Halls has said this but now you learn it.
    Absolute value is a metric, therefore it is not negative.
    $|x-a|$ is the measure of the distance from $x$ to $a$.
    $|x-5|$ is the measure of the distance from $x$ to $5$.
    $|x-3|<6$ says that $x$ is less than six units from $3$.
    $|x+8|>5$ says that $x$ is more than five units from $-8$.
    $|x+1|\le 7$ says that $x$ is at most than seven units from $-1$.
    $|x-4|\ge 7$ says that $x$ is at least seven units from $4$.
    Good study notes.
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    Super Member harpazo's Avatar
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    Re: Foreign Household Voltage

    Quote Originally Posted by HallsofIvy View Post
    $|x- 220|\le 8$ is the same as $-8\le x- 220\le 8$. Adding 220 to each part, $220- 8\le x \le 220+ 8$ or $212 \le x\le 228$.
    Your Latex reply is blocked by the message (the words).
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    Re: Foreign Household Voltage

    [QUOTE=harpazo;947381]In other countries, normal household voltage is 220 volts. It is acceptable for the actual voltage x to differ from normal by at most 8 volts. A formula that describes this is |x - 220| ≤ 8.
    A. Show that a voltage of 214 is acceptable.
    B. Show that a voltage of 209 is not acceptable.
    Question: Must I replace x with 214 and then 209 respectively for parts A and B? /QUOTE]
    To say at most means $|V-220|\le 8$.
    OR $-8 \le V-220 \le 8 $, that is the same as $212\le V\le 228$.

    Now look closely at tat last sequence of inequalities:
    $V=214$ works, while $V=209$ does not work!
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    Super Member harpazo's Avatar
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    Re: Foreign Household Voltage

    [QUOTE=Plato;947443]
    Quote Originally Posted by harpazo View Post
    In other countries, normal household voltage is 220 volts. It is acceptable for the actual voltage x to differ from normal by at most 8 volts. A formula that describes this is |x - 220| ≤ 8.
    A. Show that a voltage of 214 is acceptable.
    B. Show that a voltage of 209 is not acceptable.
    Question: Must I replace x with 214 and then 209 respectively for parts A and B? /QUOTE]
    To say at most means $|V-220|\le 8$.
    OR $-8 \le V-220 \le 8 $, that is the same as $212\le V\le 228$.

    Now look closely at tat last sequence of inequalities:
    $V=214$ works, while $V=209$ does not work!
    I totally get it now.

    Note:

    Your Latex reply is blocked by the message (the words).
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