1. ## 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?

2. ## Re: Foreign Household Voltage

Originally Posted by harpazo
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 $4$.

3. ## 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 $212 \le x\le 228$.

4. ## Re: Foreign Household Voltage

Originally Posted by Plato
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.

5. ## Re: Foreign Household Voltage

Originally Posted by HallsofIvy
$|x- 220|\le 8$ is the same as $-8\le x- 220\le 8$. Adding 220 to each part, $220- 8\le x \le 220+ 8$ or $212 \le x\le 228$.

6. ## 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!

7. ## Re: Foreign Household Voltage

[QUOTE=Plato;947443]
Originally Posted by harpazo
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.

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