Câu 1:
a: \(\dfrac{11}{19}+\dfrac{19}{18}+\dfrac{8}{19}-\dfrac{1}{18}+5,2\)
\(=\left(\dfrac{11}{19}+\dfrac{8}{19}\right)+\left(\dfrac{19}{18}-\dfrac{1}{18}\right)+5,2\)
=1+1+5,2=7,2
b: \(1\dfrac{4}{23}+\dfrac{5}{21}-\dfrac{4}{23}+0,5+\dfrac{16}{21}\)
\(=\left(1+\dfrac{4}{23}-\dfrac{4}{23}\right)+\left(\dfrac{5}{21}+\dfrac{16}{21}\right)+0,5\)
\(=1+1+0,5=2,5\)
c: \(\dfrac{3}{7}\cdot\dfrac{16}{15}-\dfrac{3}{7}\cdot\dfrac{2}{15}=\dfrac{3}{7}\left(\dfrac{16}{15}-\dfrac{2}{15}\right)\)
\(=\dfrac{3}{7}\cdot\dfrac{14}{15}=\dfrac{3}{15}\cdot\dfrac{14}{7}=\dfrac{2}{5}\)
d: \(\dfrac{3}{7}\cdot19\dfrac{1}{3}-\dfrac{3}{7}\cdot33\dfrac{1}{3}\)
\(=\dfrac{3}{7}\left(19+\dfrac{1}{3}-33-\dfrac{1}{3}\right)=\dfrac{3}{7}\cdot\left(-14\right)=-6\)
e: \(15\dfrac{1}{4}:\left(-\dfrac{5}{7}\right)-25\dfrac{1}{4}:\left(-\dfrac{5}{7}\right)\)
\(=\left(15+\dfrac{1}{4}\right)\cdot\dfrac{-7}{5}-\left(25+\dfrac{1}{4}\right)\cdot\dfrac{-7}{5}\)
\(=\dfrac{-7}{5}\left(15+\dfrac{1}{4}-25-\dfrac{1}{4}\right)=-\dfrac{7}{5}\cdot\left(-10\right)=14\)
f: \(\dfrac{4^2\cdot2^3}{2^6}=\dfrac{2^4\cdot2^3}{2^6}=\dfrac{2^7}{2^6}=2\)
g: \(9\cdot\left(-\dfrac{1}{3}\right)^3+\dfrac{1}{3}=9\cdot\dfrac{-1}{27}+\dfrac{1}{3}=-\dfrac{1}{3}+\dfrac{1}{3}=0\)
h: \(\left(\dfrac{5}{12}:3\dfrac{2}{6}\right)+\left(\dfrac{2}{3}-\dfrac{1}{2}\right)^2\)
\(=\left(\dfrac{5}{12}:\dfrac{10}{3}\right)+\left(\dfrac{4}{6}-\dfrac{3}{6}\right)^2\)
\(=\dfrac{5}{12}\cdot\dfrac{3}{10}+\left(\dfrac{1}{6}\right)^2=\dfrac{1}{8}+\dfrac{1}{36}=\dfrac{11}{72}\)
i: \(\left(-0,375\right)\cdot4\dfrac{1}{3}\cdot\left(-2\right)^3=\dfrac{-3}{8}\cdot\dfrac{13}{3}\cdot\left(-8\right)=13\)
k:
\(\dfrac{8}{9}+\dfrac{15}{23}+\dfrac{1}{9}+\dfrac{-15}{23}+\dfrac{1}{2}\)
\(=\left(\dfrac{8}{9}+\dfrac{1}{9}\right)+\left(\dfrac{15}{23}-\dfrac{15}{23}\right)+\dfrac{1}{2}\)
\(=1+\dfrac{1}{2}=\dfrac{3}{2}\)
l: \(16\dfrac{2}{7}:\dfrac{-3}{5}-28\dfrac{2}{7}:\dfrac{-3}{5}\)
\(=\left(16+\dfrac{2}{7}-28-\dfrac{2}{7}\right):\dfrac{-3}{5}=-12\cdot\dfrac{5}{-3}=\dfrac{60}{3}=20\)
m: \(\dfrac{1}{2}\cdot\sqrt{64}-\sqrt{\dfrac{4}{25}}+1^{2012}\)
\(=\dfrac{1}{2}\cdot8-\dfrac{2}{5}+1=4-\dfrac{2}{5}+1=5-\dfrac{2}{5}=\dfrac{23}{5}\)
Câu 2:
a: \(\dfrac{3}{4}+\dfrac{2}{5}x=\dfrac{29}{60}\)
=>\(\dfrac{2}{5}x=\dfrac{29}{60}-\dfrac{3}{4}=\dfrac{29}{60}-\dfrac{45}{60}=-\dfrac{16}{60}=-\dfrac{8}{15}\)
=>\(x=-\dfrac{8}{15}:\dfrac{2}{5}=-\dfrac{8}{15}\cdot\dfrac{5}{2}=-\dfrac{40}{30}=-\dfrac{4}{3}\)
b: \(\dfrac{1}{2}x+\sqrt{0,04}=\sqrt{1,96}\)
=>\(\dfrac{x}{2}+0,2=1,4\)
=>\(\dfrac{x}{2}=1,4-0,2=1,2\)
=>\(x=1,2\cdot2=2,4\)
c: \(\dfrac{1}{4}:\dfrac{1}{4}+x=5\)
=>x+1=5
=>x=5-1=4
d: \(\left(\dfrac{1}{4}+x\right)^2=25\)
=>\(\left[{}\begin{matrix}x+\dfrac{1}{4}=5\\x+\dfrac{1}{4}=-5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5-\dfrac{1}{4}=\dfrac{19}{4}\\x=-5-\dfrac{1}{4}=-\dfrac{21}{4}\end{matrix}\right.\)
e: ĐKXĐ: x>=1
\(\sqrt{x-1}=5\)
=>\(x-1=5^2=25\)
=>x=25+1=26
f: 1,2x-2=2,4-x
=>1,2x+x=2,4+2
=>2,2x=4,4
=>x=2
g: 2x-5=x+7
=>2x-x=5+7
=>x=12
h: \(\dfrac{31}{36}-\left(\dfrac{1}{3}-x\right)^2=\dfrac{5}{6}\)
=>\(\left(x-\dfrac{1}{3}\right)^2=\dfrac{31}{36}-\dfrac{5}{6}=\dfrac{31}{36}-\dfrac{30}{36}=\dfrac{1}{36}\)
=>\(\left[{}\begin{matrix}x-\dfrac{1}{3}=\dfrac{1}{6}\\x-\dfrac{1}{3}=-\dfrac{1}{6}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{6}+\dfrac{1}{3}=\dfrac{3}{6}=\dfrac{1}{2}\\x=-\dfrac{1}{6}+\dfrac{1}{3}=-\dfrac{1}{6}+\dfrac{2}{6}=\dfrac{1}{6}\end{matrix}\right.\)
i: \(\left(2x-3\right)\left(\dfrac{3}{4}x+1\right)=0\)
=>\(\left[{}\begin{matrix}2x-3=0\\\dfrac{3}{4}x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=3\\\dfrac{3}{4}x=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=-1:\dfrac{3}{4}=-\dfrac{4}{3}\end{matrix}\right.\)
k: \(2^x+2^{x+3}=144\)
=>\(2^x+2^x\cdot8=144\)
=>\(9\cdot2^x=144\)
=>\(2^x=\dfrac{144}{9}=16=2^4\)
=>x=4
m: ĐKXĐ: x>=-1
\(3\sqrt{x+1}-1=38\)
=>\(3\sqrt{x+1}=38+1=39\)
=>\(\sqrt{x+1}=13\)
=>x+1=169
=>x=168(nhận)
