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\(\Rightarrow x+3=8\Rightarrow x=5\Rightarrow y=\dfrac{1}{3}x=\dfrac{5}{3}\)
\(\left\{{}\begin{matrix}x=3y\\x+\dfrac{9}{3}=8\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=3y\\x+3=8\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}5=3y\\x=5\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{5}{3}\\x=5\end{matrix}\right.\)
a) \(\frac{x+1}{3}=\frac{x-2}{4}\)
=> (x+1).4 = (x - 2) . 3
=> 4x + 4 = 3x - 6
=> 4x - 3x = - 6 - 4
=> x = - 10
b) \(\frac{x-6}{7}+\frac{x-7}{8}+\frac{x-8}{9}=\frac{x-9}{10}+\frac{x-10}{11}+\frac{x-11}{12}\)
\(\Rightarrow\left(\frac{x-6}{7}+1\right)+\left(\frac{x-7}{8}+1\right)+\left(\frac{x-8}{9}+1\right)=\left(\frac{x-9}{10}+1\right)+\left(\frac{x-10}{11}+1\right)+\left(\frac{x-11}{12}+1\right)\)
\(\Rightarrow\frac{x+1}{7}+\frac{x+1}{8}+\frac{x+1}{9}=\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}\)
\(\Rightarrow\frac{x+1}{7}+\frac{x+1}{8}+\frac{x+1}{9}-\frac{x+1}{10}-\frac{x+1}{11}-\frac{x+1}{12}\) = 0
\(\Rightarrow\left(x+1\right).\left(\frac{1}{7}+\frac{1}{8}+\frac{1}{9}-\frac{1}{10}-\frac{1}{11}-\frac{1}{12}\right)\)
Vì \(\frac{1}{7}+\frac{1}{8}+\frac{1}{9}-\frac{1}{10}-\frac{1}{11}-\frac{1}{12}\ne0\) nên x + 1 =0
=> x = -1
c) Xem lại đề
(x+3)/7 thì bạn cộng thêm 7/7 vào, tương tự thì cộng 8/7, 9/7,.. Đén đây thì quy đồng rồi rút gọn. tự nghĩ nhé
Ta có : \(\frac{x+3}{7}+\frac{x+3}{8}+\frac{x+3}{9}+\frac{x+3}{10}=\frac{x+3}{11}\)
\(\Leftrightarrow\frac{x+3}{7}+\frac{x+3}{8}+\frac{x+3}{9}+\frac{x+3}{10}-\frac{x+3}{11}=0\)
\(\Leftrightarrow\left(x+3\right)\left(\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}-\frac{1}{11}\right)=0\)
Mà : \(\left(\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}-\frac{1}{11}\right)\ne0\)
Nên : x + 3 = 0
=> x = -3
\(\frac{11}{15}-\left(\frac{7}{9}+x\right)\frac{3}{8}=\frac{61}{90}+\frac{x}{3}\)
\(\frac{11}{15}-\frac{7}{24}-\frac{3}{8}x=\frac{61}{90}+\frac{x}{3}\)
\(\frac{x}{3}+\frac{3}{8}x=\frac{11}{15}-\frac{7}{24}-\frac{61}{90}\)
\(\frac{17}{24}x=-\frac{17}{72}\)
\(\Rightarrow x=-\frac{1}{3}\)
\(\frac{x+4}{8}+\frac{x+3}{9}=\frac{x+2}{10}+\frac{x+1}{11}\)
\(\Leftrightarrow\frac{x+4}{8}+1+\frac{x+3}{9}+1=\frac{x+2}{10}+1+\frac{x+1}{11}+1\)
\(\Leftrightarrow\frac{x+12}{8}+\frac{x+12}{9}=\frac{x+12}{10}+\frac{x+12}{11}\)
\(\Leftrightarrow\frac{x+12}{8}+\frac{x+12}{9}-\frac{x+12}{10}-\frac{x+12}{11}=0\)
\(\Leftrightarrow\left(x+12\right)\left(\frac{1}{8}+\frac{1}{9}-\frac{1}{10}-\frac{1}{11}\right)=0\)
Mà: \(\frac{1}{8}+\frac{1}{9}-\frac{1}{10}-\frac{1}{11}\ne0\)
\(\Rightarrow x+12=0\)
\(\Rightarrow x=-12\)