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September 27th, 2018, 01:32 AM  #1 
Newbie Joined: Sep 2018 From: Spain Posts: 17 Thanks: 0  Need some serious help with this equation!! please!!
This is the equation 3x  1/2  4x  3 = 5 A guy and youtube told me this That looks strange, but the process is the same as other absolute value equations You have to get everything except the absolute value part on one side of the equation. Then to get rid of the absolute value vertical bars, you set up two cases: one case is equal to what you have, and the other case is equal to the negative version of what you have. Typing here is a terrible way to try to explain the steps. there are a lot of fractions, to keep up with. I ended up getting 5/2 and 13/2 for x, and they both checked out. Wish I had a way to show the steps. But I need the steps and guidelines because I am completely lost. Last edited by skipjack; September 27th, 2018 at 02:47 AM. 
September 27th, 2018, 02:58 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,966 Thanks: 2216 
To solve 3x  1/2  4x  3 = 5, solve 3x  1/2  4(x  3) = 5 and 3x  1/2 + 4(x  3) = 5. The first equation gives x  1/2 + 12 = 5, so x = 13/2, which satisfies the original equation, as 13/2  3 > 0. The second equation gives 7x  1/2  12 = 5, so x = 5/2, which also satisfies the original equation, as 5/2  3 < 0. Last edited by skipjack; September 27th, 2018 at 11:56 AM. 
September 27th, 2018, 03:09 AM  #3 
Newbie Joined: Sep 2018 From: Spain Posts: 17 Thanks: 0 
wow great! but whats the formula for that ? to be able to solve the equation?

September 27th, 2018, 10:03 AM  #4  
Senior Member Joined: Oct 2016 From: Arizona Posts: 209 Thanks: 37 Math Focus: I'm still deciding, but my recent focus has been olympiad problems and math journal problems.  Quote:
Or, you can think of it like this; it means that $x=5$ or $x=5$. It all goes back to the actual meaning of absolute value! The same idea can be used to solve more complicated equations. Last edited by ProofOfALifetime; September 27th, 2018 at 10:06 AM.  
September 27th, 2018, 10:05 AM  #5  
Senior Member Joined: Oct 2016 From: Arizona Posts: 209 Thanks: 37 Math Focus: I'm still deciding, but my recent focus has been olympiad problems and math journal problems.  Quote:
 
September 27th, 2018, 11:57 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,966 Thanks: 2216 
Yes. I've corrected it.


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