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\(\frac{x+10}{30}+\frac{x+14}{43}+\frac{x+5}{95}+\frac{x+130}{5}=0\)
\(\Leftrightarrow\left(\frac{x+10}{30}+3\right)+\left(\frac{x+14}{43}+2\right)+\left(\frac{x+5}{95}+1\right)+\left(\frac{x+130}{5}-6\right)=0\)
\(\Leftrightarrow\frac{x+10+90}{30}+\frac{x+14+86}{43}+\frac{x+5+95}{95}+\frac{x+130-30}{5}=0\)
\(\Leftrightarrow\frac{x+100}{30}+\frac{x+100}{43}+\frac{x+100}{95}+\frac{x+100}{5}=0\)
\(\Leftrightarrow\left(x+100\right)\left(\frac{1}{30}+\frac{1}{43}+\frac{1}{95}+\frac{1}{5}\right)=0\)
Vì \(\frac{1}{30}+\frac{1}{43}+\frac{1}{95}+\frac{1}{5}\ne0\)
=> x + 100 = 0
=> x = -100
Ta có: x-10/30 + x-14/43 + x-5/95 + x-148/8 = 0
ð X-10/30 - 3 + x-14/43 - 2 + x-5/95 - 1 + x-148/8 + 6 = 0
ð X-10-90/30 + x-14-86/43 + x-5-95/95 + x-148+48/8 = 0
ð X-100/30 + X-100/43 + X-100/95 + X-100/8 = 0
ð {X-100} . {1/30 + 1/43 + 1/95 + 1/8} = 0
Vì: /30 + 1/43 + 1/95 + 1/8 khác 0
ð X-100 = 0
ð X = 100
a) \(\frac{1}{2}+\frac{2}{3}:x=\frac{3}{4}\)
=> \(\frac{2}{3}:x=\frac{3}{4}-\frac{1}{2}\)
=> \(\frac{2}{3}:x=\frac{1}{4}\)
=> \(x=\frac{2}{3}:\frac{1}{4}=\frac{8}{3}\)
b) \(5,4-3\left|x-\frac{21}{10}\right|=0\)
=> \(3\left|x-\frac{21}{10}\right|=\frac{27}{5}\)
=> \(\left|x-\frac{21}{10}\right|=\frac{27}{5}:3=\frac{9}{5}\)
=> \(\left|x-\frac{21}{10}\right|=\frac{9}{5}\)
Trường hợp 1 : \(x-\frac{21}{10}=\frac{9}{5}\)
=> \(x=\frac{9}{5}+\frac{21}{10}=\frac{39}{10}\)
Trường hợp 2 : \(x-\frac{21}{10}=-\frac{9}{5}\)
=> \(x=-\frac{9}{5}+\frac{21}{10}=\frac{3}{10}\)
Vậy : ...
c) \(10\sqrt{x-5}=25\)
=> \(\sqrt{x-5}=\frac{5}{2}\)
=> \(\left(x-5\right)^2=\frac{25}{4}\)
Trường hợp 1 :
\(x-5=\frac{25}{4}\)=> \(x=\frac{25}{4}+5=\frac{45}{4}\)
Trường hợp 2 :
\(x-5=-\frac{25}{4}\)=> \(x=-\frac{25}{4}+5=-\frac{5}{4}\)(loại)
Vậy \(x=\frac{45}{4}\)