a) \(\dfrac{2}{3}\cdot n+\dfrac{3}{4}\cdot n=\dfrac{17}{6}\)
\(\Rightarrow n\cdot\left(\dfrac{2}{3}+\dfrac{3}{4}\right)=\dfrac{17}{6}\)
\(\Rightarrow n\cdot\dfrac{1}{2}=\dfrac{17}{6}\)
\(\Rightarrow n=\dfrac{17}{6}:\dfrac{1}{2}\)
\(\Rightarrow n=\dfrac{17}{3}\)
b) \(\dfrac{1}{5}\cdot n+\dfrac{7}{15}=\dfrac{1}{3}n\)
\(\Rightarrow\dfrac{1}{3}\cdot n-\dfrac{1}{5}\cdot n=\dfrac{7}{15}\)
\(\Rightarrow\left(\dfrac{1}{3}-\dfrac{1}{5}\right)n=\dfrac{7}{15}\)
\(\Rightarrow\dfrac{2}{15}n=\dfrac{7}{15}\)
\(\Rightarrow n=\dfrac{7}{15}:\dfrac{2}{15}\)
\(\Rightarrow n=\dfrac{7}{2}\)
c) \(\dfrac{4}{21}-\dfrac{2}{3}\cdot n=\dfrac{3}{7}\cdot n\)
\(\Rightarrow\dfrac{3}{7}\cdot n+\dfrac{2}{3}\cdot n=\dfrac{4}{21}\)
\(\Rightarrow\left(\dfrac{3}{7}+\dfrac{2}{3}\right)\cdot n=\dfrac{4}{21}\)
\(\Rightarrow\dfrac{23}{21}\cdot n=\dfrac{4}{21}\)
\(\Rightarrow n=\dfrac{4}{21}:\dfrac{23}{21}\)
\(\Rightarrow n=\dfrac{4}{23}\)
a: =>n(2/3+3/4)=17/6
=>n*17/12=17/6
=>n=17/6:17/12=2
b: =>1/5n-1/3n=-7/15
=>-2/15n=-7/15
=>n=7/15:2/15=7/15*15/2=7/2
c: =>3/7n+2/3n=4/21
=>9/21n+14/21n=4/21
=>9n+14n=4
=>23n=4
=>n=4/23
