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February 17th, 2018, 11:01 AM   #1
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Post I need help with this equation, it's URGENT.

I need to solve this exercise using the absolute value properties. The result must be in the form of an interval.
I would appreciate it if you could send the solution written on a piece of paper.

Thanks!!!...

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February 17th, 2018, 11:20 AM   #2
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$\begin{align*}
&\text{OK IT'S ON THE WAY!!!!}\\ \\

&\text{I ADDRESSED IT TO A HOUSE WITH DOORS AND WINDOWS} \\ \\

&\text{I'D GO WAIT BY THE MAILBOX UNTIL IT ARRIVES!}

\end{align*}$
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Last edited by romsek; February 17th, 2018 at 11:22 AM.
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February 17th, 2018, 11:31 AM   #3
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but seriously folks...

$|x+2| = |x+7|$

you can split this into 3 areas

$x < -7$

$-7 \leq x \leq -2$

$-2 < x$

In area 1 we have

$-(x+2) = -(x+7)$

$x+2 = x+7$

$0 = 5$

and thus there are no solutions to this equation in area 1

In area 2 we have

$-(x+2) = x+7$

$-x -2 = x+7$

$-9 = 2x$

$x = -\dfrac 9 2$

In area 3 we have

$(x+2) = (x+7)$

and again it should be clear that there are no solutions to this in area 3

So there is only one solution to this equation and that is

$x = -\dfrac 9 2$

You talk about wanting the solution as intervals. This suggests to me that the expression in question should actually be an inequality. Not an equality.

Have you expressed the question correctly?
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February 17th, 2018, 11:35 AM   #4
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HINT: $|x + 2| = |x + 7| \implies x + 2 = x + 7 \text { or } x + 2 = -\ (x + 7).$

Now what?
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February 17th, 2018, 11:37 AM   #5
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It's not my equation, but I want to understand the solution in the beginning part:

but seriously folks...

$|x+2| = |x+7|$

you can split this into 3 areas

*$x < -7$

*$-7 \leq x \leq -2$

*$-2 < x$

In what way you get the (*) inequation?

Last edited by skipjack; February 17th, 2018 at 06:56 PM.
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February 17th, 2018, 12:08 PM   #6
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Quote:
Originally Posted by shaharhada View Post
It's not my equation, but I want to understand the solution in the beginning part:

but seriously folks...

$|x+2| = |x+7|$

you can split this into 3 areas

*$x < -7$

*$-7 \leq x \leq -2$

*$-2 < x$

In what way you get the (*) inequation?
I specified 3 separate sub-domains. There is no derivation involved.

Last edited by skipjack; February 17th, 2018 at 06:56 PM.
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February 17th, 2018, 12:09 PM   #7
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Quote:
Originally Posted by JeffM1 View Post
Now what?
DisneyWorld?
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February 17th, 2018, 01:39 PM   #8
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Quote:
Originally Posted by maverick71 View Post
solution written on a piece of paper.
solution
---------
paper/x
where x > 1
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February 17th, 2018, 04:20 PM   #9
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Math Focus: Yet to find out.
. Damn this forum is good.
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February 17th, 2018, 04:38 PM   #10
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Quote:
Originally Posted by romsek View Post
DisneyWorld?
No thanks. Went in January ... an expensive lesson in “hurry up & wait”
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