Question

x+2014 /2 +2x+4028/7=x+2014/5+x+2014/6

Answer 1

\(\frac{x+2014}{2}+\frac{2x+4028}{7}=\frac{x+2014}{5}+\frac{x+2014}{6}\)

<=> \(\frac{x+2014}{2}+\frac{2\left(x+2014\right)}{7}=\frac{x+2014}{5}+\frac{x+2014}{6}\)

<=> \(\frac{x+2014}{2}+\frac{x+2014}{\frac{7}{2}}=\frac{x+2014}{5}+\frac{x+2014}{6}\)

<=> \(\frac{x+2014}{2}+\frac{x+2014}{\frac{7}{2}}-\frac{x+2014}{5}-\frac{x+2014}{6}=0\)

<=> \(\left(x+2014\right)\left(\frac{1}{2}+\frac{1}{\frac{7}{2}}-\frac{1}{5}-\frac{1}{6}\right)=0\)

Vì \(\frac{1}{2}+\frac{1}{\frac{7}{2}}-\frac{1}{5}-\frac{1}{6}\ne0\)

=> x + 2014 = 0 <=> x = -2014

Answer 2

Bài làm :

\(\frac{x+2014}{2}+\frac{2x+4028}{7}=\frac{x+2014}{5}+\frac{x+2014}{6}\)

\(\Rightarrow\frac{x+2014}{2}+\frac{2x+4028}{7}-\frac{x+2014}{5}-\frac{x+2014}{6}=0\)

\(\Rightarrow\frac{x+2014}{2}+\frac{2.\left(x+2014\right)}{7}-\frac{x+2014}{5}-\frac{x+2014}{6}=0\)

\(\Rightarrow\left(x+2014\right).\left(\frac{1}{2}+\frac{2}{7}-\frac{1}{5}-\frac{1}{6}\right)=0\)

\(\Rightarrow x+2014=0:\left(\frac{1}{2}+\frac{2}{7}-\frac{1}{5}-\frac{1}{6}\right)\)

\(\Rightarrow x+2014=0\)

\(\Rightarrow x=-2014\)

Vậy x = - 2014 .

Học tốt nhé