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September 27th, 2018, 02:32 AM   #1
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Need some serious help with this equation!! please!!

This is the equation

3x - 1/2 - 4|x - 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 03:47 AM.
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September 27th, 2018, 03:58 AM   #2
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To solve 3x - 1/2 - 4|x - 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.
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Last edited by skipjack; September 27th, 2018 at 12:56 PM.
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September 27th, 2018, 04:09 AM   #3
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wow great! but whats the formula for that ? to be able to solve the equation?
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September 27th, 2018, 11:03 AM   #4
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Math Focus: Frame Theory is pretty awesome, and it's ripe for undergraduate research!
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Originally Posted by raven2k7 View Post
wow great! but whats the formula for that ? to be able to solve the equation?
It might help you to start with some very simple absolute value equations and work your way up. Basically, start with this question. What does $|x|=5$ mean? It gives you two solutions $x=5$ and $x=-5$.

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 11:06 AM.
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September 27th, 2018, 11:05 AM   #5
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Math Focus: Frame Theory is pretty awesome, and it's ripe for undergraduate research!
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Originally Posted by skipjack View Post
To solve 3x - 1/2 - 4|x - 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.
I think you meant to write 3x - 1/2 + 4(x - 3) = 5 for the second one.
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September 27th, 2018, 12:57 PM   #6
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Yes. I've corrected it.
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