Find the sum of the solutions: 5│x│ - 3 = │3x + 7│

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Find the sum of the solutions: 5│x│ - 3 = │3x + 7│

Mathematics
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\[5\left| x \right|-3 = \left| 3x+7 \right|\]
How would I go about this?
Are things in absolute value "like terms?"

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Let's consider some cases: ------------------------------------------- \[\text{ CASE 1:} x>0 ; x>\frac{-7}{3}\] |x|=x ; |3x+7|=3x+7 5(x)-3=3x+7 solve this for x and then check it -------------------------------------------- \[\text{ CASE 2:} x>0; x<\frac{-7}{3}\] |x|=x; |3x+7|=-(3x+7) 5(x)-3=-(3x+7) solve this for x and check it -------------------------------------------- \[\text{ CASE 3: } x<0; x>\frac{-7}{3}\] |x|=-x ; |3x+7|=3x+7 5(-x)-3=3x+7 solve this for x and check it -------------------------------------------- \[\text{ CASE 4: } x<0 ; x<\frac{-7}{3}\] |x|=-x; |3x+7|=-(3x+7) 5(-x)-3=-(3x+7) solve this for x and check it
Is that how you have to do it?
and i dont understand the "Cases"
i'm looking at when |x|=x or when it is |x|=-x and something for |3x+7|
what do you mean by something for │3x + 7│
same thing*
Can you try to explain it a different way. I'm sorry
|3x+7|=3x+7 when 3x+7>0 |3x+7|=-(3x+7) when 3x+7<0 |x|=x when x>0 |x|=-x when x<0
i looked at all possible combinations of these
that is how i got my 4 cases
Okay. Thanks. It's more clear now.
i actually wrote this above when i did the 4 cases
3x+7>0 => x>-7/3 after solve for x 3x+7<0 => x<-7/3 after solving for x
i'm glad you understand though :)

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