February 17th, 2018, 11:01 AM  #1 
Newbie Joined: Feb 2018 From: in a house with doors and windows Posts: 1 Thanks: 0  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!!!... Math.png 
February 17th, 2018, 11:20 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,790 Thanks: 923 
$\begin{align*} &\text{OK IT'S ON THE WAY!!!!}\\ \\ &\text{I ADDRESSED IT TO A HOUSE WITH DOORS AND WINDOWS} \\ \\ &\text{I'D GO WAIT BY THE MAILBOX UNTIL IT ARRIVES!} \end{align*}$ Last edited by romsek; February 17th, 2018 at 11:22 AM. 
February 17th, 2018, 11:31 AM  #3 
Senior Member Joined: Sep 2015 From: USA Posts: 1,790 Thanks: 923 
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? 
February 17th, 2018, 11:35 AM  #4 
Senior Member Joined: May 2016 From: USA Posts: 923 Thanks: 369 
HINT: $x + 2 = x + 7 \implies x + 2 = x + 7 \text { or } x + 2 = \ (x + 7).$ Now what? 
February 17th, 2018, 11:37 AM  #5 
Senior Member Joined: Nov 2011 Posts: 184 Thanks: 2 
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. 
February 17th, 2018, 12:08 PM  #6 
Senior Member Joined: Sep 2015 From: USA Posts: 1,790 Thanks: 923  I specified 3 separate subdomains. There is no derivation involved.
Last edited by skipjack; February 17th, 2018 at 06:56 PM. 
February 17th, 2018, 12:09 PM  #7 
Senior Member Joined: Sep 2015 From: USA Posts: 1,790 Thanks: 923  
February 17th, 2018, 01:39 PM  #8 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,862 Thanks: 768  
February 17th, 2018, 04:20 PM  #9 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,541 Thanks: 516 Math Focus: Yet to find out.  . Damn this forum is good.

February 17th, 2018, 04:38 PM  #10 
Math Team Joined: Jul 2011 From: Texas Posts: 2,724 Thanks: 1378  

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calculus, equation, math or calculus, trigonometry or algebra, urgent 
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