Question

Giải PT:

\(\dfrac{3x-40}{50}+\dfrac{3x-10}{40}+\dfrac{x+30}{20}+\dfrac{x-90}{10}=0\)

Answer 1

\(\left(\dfrac{3x-40}{50}\right)+\left(\dfrac{3x-10}{40}\right)+\dfrac{x+30}{20}+\dfrac{x-90}{10}=0\)

=>\(\left(\dfrac{3x-40}{50}-1\right)+\left(\dfrac{3x-10}{40}-2\right)+\dfrac{x+30}{20}-3+\dfrac{x-90}{10}=0\)

=>\(\dfrac{3x-90}{50}+\dfrac{3x-90}{40}+\dfrac{x-90}{10}+\dfrac{x-30}{20}=0\)

=>\(\dfrac{-x+90}{10}=\left(x-30\right)\left(\dfrac{3}{50}+\dfrac{3}{40}+\dfrac{1}{20}\right)\)

=>\(\dfrac{-x+90}{10}=\left(x-30\right)\cdot\dfrac{37}{200}\)

=>\(-x+90=\dfrac{37}{20}\left(x-30\right)\)

=>\(\dfrac{37}{20}x-555=-x+90\)

=>\(\dfrac{57}{20}x=90+555=645\)

=>\(x=645:\dfrac{57}{20}=\dfrac{4300}{19}\)