Question

Dizzy question:

|3x-7|=|5x+3|

how do I solve this?

Answer 1

solve two equations, that is it
first solve
\[3x-7=5x+3\] then solve
\[-3x+7=5x+3\] those will give your two answers

Answer 2

ok but how about the right side... do we have to change its sign too ? ... if not , why?

Answer 3

well you can if you like, and you will get 4 equations to solve.
but then you will see that you really get the same two equations twice

Answer 4

what you have is \(|a|=|b|\) so \(a=b\) or \(a=-b\)
if you write down
\[a=b\]
\[a=-b\]
\[-a-b\]
\[-a=-b\] you see that the bottom two are identical to the top two

Answer 5

actually the word is "equavalent" bottom two are equivalent to top two

Answer 6

ahh .. I see, Thanks a lot, :) , I always had in absolute value only one side of the equation, never twice. And that's why I had some doubts lol. Thank you very much @satellite73

Answer 7

never both of them :$ ... (My english sucks !)

Answer 8

\[\Large 3x-7=5x+3\]\[\Large 3x-5x=3+7\]\[\Large -2x=10\]\[\Large x=-5 \]

\[-3x+7=5x+3\]\[-8x=-4\]\[x=\frac12\]
lol... :P