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\(a,\frac{-3}{2}-2x+\frac{3}{4}=-1\)
\(\frac{-3}{2}-2x=-1-\frac{3}{4}\)
\(\frac{-3}{2}-2x=\frac{-7}{4}\)
\(2x=\frac{-7}{4}+\frac{-3}{2}\)
\(2x=\frac{-13}{4}\)
\(x=\frac{-13}{4}:2\)
\(x=\frac{-13}{4}.\frac{1}{2}\)
\(x=\frac{-13}{8}\)
b) \(3^{n+3}+3^{n+1}+2^{n+3}+2^{n+2}=3^{n+1}\left(3^2+1\right)+2^{n+2}\left(2+1\right)\)
=\(3^{n+1}.2.5+2^{n+2}.3\)=\(2.3\left(3^n+2^{n+1}\right)⋮6\)
=> dpcm
a: \(\dfrac{2}{5}+\dfrac{3}{5}:\left(-\dfrac{3}{2}\right)+\dfrac{1}{2}\)
\(=\dfrac{2}{5}+\dfrac{3}{5}\cdot\dfrac{-2}{3}+\dfrac{1}{2}\)
\(=\dfrac{2}{5}-\dfrac{2}{5}+\dfrac{1}{2}=\dfrac{1}{2}\)
b: \(2,5-\left(-\dfrac{5}{6}\right)^0+\left(-\dfrac{1}{6}\right)^2\cdot\left(-3\right)\)
\(=\dfrac{5}{2}-1+\dfrac{1}{36}\cdot\left(-3\right)\)
\(=\dfrac{3}{2}-\dfrac{1}{12}=\dfrac{18}{12}-\dfrac{1}{12}=\dfrac{17}{12}\)
\(=6.\frac{-8}{27}-3.\frac{4}{9}-2.\frac{-2}{3}+4\)
\(=\frac{-16}{9}-\frac{4}{3}+\frac{4}{3}+4\)
\(=\frac{20}{9}\)
\(6\cdot\left(-\frac{2}{3}\right)^3-3\cdot\left(-\frac{2}{3}\right)^2-2\cdot\left(-\frac{2}{3}\right)+4\)
\(=6\cdot\left(-\frac{8}{27}\right)-3\cdot\frac{4}{9}-2\cdot\left(-\frac{2}{3}\right)+4\)
\(=-\frac{48}{27}-\frac{12}{9}+\frac{4}{3}+4\)
\(=-\frac{28}{9}+\frac{4}{3}+4\)
\(=-\frac{16}{9}+4\)
\(=\frac{20}{9}\)