Câu 8:
\(a,\sqrt{\dfrac{9}{4}}-\left(\dfrac{2}{3}-\dfrac{3}{2}\right)^2+\left(-1\right)^{2017}+\left|-5\right|\)
\(=\dfrac{3}{2}-\left(\dfrac{4}{6}-\dfrac{9}{6}\right)^2+\left(-1\right)+5\)
\(=\dfrac{3}{2}-\left(\dfrac{-5}{6}\right)^2+\left(-1\right)+5\)
\(=\dfrac{3}{2}-\dfrac{25}{36}+\left(-1\right)+5\)
\(=\dfrac{54}{36}-\dfrac{25}{36}+\dfrac{-36}{36}+\dfrac{180}{36}\)
\(=\dfrac{173}{36}\)
\(b,\dfrac{-17}{15}.\dfrac{5}{8}+\dfrac{-13}{15}.\dfrac{5}{8}+\dfrac{1}{4}\)
\(=\dfrac{5}{8}.\left(\dfrac{-17}{15}+\dfrac{-13}{15}\right)+\dfrac{1}{4}\)
\(=\dfrac{5}{8}.\dfrac{-30}{15}+\dfrac{1}{4}\)
\(=\dfrac{-5}{4}+\dfrac{1}{4}\)
\(=\dfrac{-4}{4}=-1\)
\(c,\left[\left(\dfrac{3}{8}-\dfrac{5}{12}\right).\left|6\right|+\left(\dfrac{1}{3}\right)^2\right].\sqrt{16}\)
\(=\left[\left(\dfrac{9}{24}-\dfrac{10}{24}\right).6+\dfrac{1}{9}\right].4\)
\(=\left[\dfrac{-1}{24}.6+\dfrac{1}{9}\right].4\)
\(=\left[\dfrac{-1}{4}+\dfrac{1}{9}\right].4\)
\(=\dfrac{-5}{36}.4\)
\(=\dfrac{-5}{9}\)
Câu 9:
a: \(\dfrac{2}{3}-0,5x=\sqrt{\dfrac{36}{9}}\)
=>\(\dfrac{2}{3}-\dfrac{x}{2}=\sqrt{4}=2\)
=>\(\dfrac{x}{2}=\dfrac{2}{3}-2=-\dfrac{4}{3}\)
=>\(x=-\dfrac{4}{3}\cdot2=-\dfrac{8}{3}\)
b: \(\left|2x+1,5\right|-\dfrac{3}{2}=\dfrac{5}{2}\)
=>\(\left|2x+1,5\right|=\dfrac{5}{2}+\dfrac{3}{2}=\dfrac{8}{2}=4\)
=>\(\left[{}\begin{matrix}2x+1,5=4\\2x+1,5=-4\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}2x=4-1,5=2,5\\2x=-4-1,5=-5,5\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=\dfrac{2.5}{2}=1,25\\x=\dfrac{-5,5}{2}=-2,75\end{matrix}\right.\)
c: \(\left|\dfrac{3}{4}-x\right|=\dfrac{5}{4}\)
=>\(\left|x-\dfrac{3}{4}\right|=\dfrac{5}{4}\)
=>\(\left[{}\begin{matrix}x-\dfrac{3}{4}=\dfrac{5}{4}\\x-\dfrac{3}{4}=-\dfrac{5}{4}\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=\dfrac{5}{4}+\dfrac{3}{4}=\dfrac{8}{4}=2\\x=-\dfrac{5}{4}+\dfrac{3}{4}=-\dfrac{2}{4}=-\dfrac{1}{2}\end{matrix}\right.\)