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a)\(\frac{x}{108}=\frac{-7}{9}.\frac{5}{6}\)
\(\frac{x}{108}=\frac{-35}{54}\)
\(\frac{x}{108}=\frac{-70}{108}\)
\(x=-70\)
b)
\(\frac{x+5}{95}+\frac{x+6}{94}+\frac{x+7}{93}+\frac{x+8}{92}+\frac{x+9}{91}=-5\)
\(\left(\frac{x+5}{95}+1\right)+\left(\frac{x+6}{94}+1\right)+\left(\frac{x+7}{93}+1\right)+\left(\frac{x+8}{92}+1\right)+\left(\frac{x+9}{91}+1\right)=-5+5=0\)
a) \(x-\frac{5}{7}=\frac{1}{9}\Rightarrow x=\frac{1}{9}+\frac{5}{7}\Rightarrow x=\frac{52}{63}\)
b) \(\frac{-3}{7}-x=\frac{4}{5}+\frac{-2}{3}\Rightarrow\frac{-3}{7}-x=\frac{2}{15}\Rightarrow x=\frac{-3}{7}-\frac{2}{15}\Rightarrow x=\frac{-59}{105}\)
c) \(x-\frac{1}{5}=\frac{2}{7}.\frac{-11}{5}\Rightarrow x-\frac{1}{5}=\frac{-22}{35}\Rightarrow x=\frac{-22}{35}+\frac{1}{5}\Rightarrow x=\frac{-3}{7}\)
d) \(\frac{x}{182}=\frac{-6}{14}.\frac{35}{91}\Rightarrow\frac{x}{182}=\frac{-15}{91}\Rightarrow x=\frac{\left(-15\right).182}{91}\Rightarrow x=-30\)
\(b.\frac{1}{3}+\frac{3}{35}< \frac{x}{210}< \frac{4}{7}+\frac{3}{5}+\frac{1}{3}\)
\(\Leftrightarrow\frac{35+9}{105}< \frac{x}{210}< \frac{60+63+35}{105}\)
\(\Leftrightarrow\frac{44}{105}< \frac{x}{210}< \frac{158}{105}\)
\(\Leftrightarrow\frac{88}{210}< \frac{x}{210}< \frac{316}{210}\)
Suy ra \(x\in\left\{89;90;100;...;313;314;315\right\}\)
\(c.\left(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}\right)-x+\frac{221}{231}=\frac{4}{3}\)
\(\Leftrightarrow\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\right)-x+\frac{221}{231}=\frac{4}{3}\)
\(\Leftrightarrow\frac{1}{11}-\frac{1}{21}-x+\frac{221}{231}=\frac{4}{3}\)
\(\Leftrightarrow\frac{21-11-231x+221}{231}=\frac{308}{231}\)
\(\Leftrightarrow-231x=308-21+11-221\)
\(\Leftrightarrow-231x=77\)
\(\Leftrightarrow x=-\frac{77}{231}=-\frac{1}{3}\)
^^
\(\frac{x}{108}=-\frac{7}{9}.\frac{5}{6}\)
\(\frac{x}{108}=-\frac{35}{54}\)
\(\Rightarrow x=\frac{108.-35}{54}=-70\)
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