Câu 1:
a) \(3\dfrac{14}{19}+\dfrac{13}{17}+\dfrac{35}{43}+6\dfrac{5}{19}+\dfrac{8}{43}\)
\(=\dfrac{71}{19}+\dfrac{13}{17}+\dfrac{35}{43}+\dfrac{119}{19}+\dfrac{8}{43}\)
\(=\left(\dfrac{71}{19}+\dfrac{119}{19}\right)+\left(\dfrac{35}{43}+\dfrac{8}{43}\right)+\dfrac{13}{17}\)
\(=10+1+\dfrac{13}{17}\)
\(=\dfrac{200}{17}\)
b) \(\dfrac{-5}{7}.\dfrac{2}{11}+\dfrac{-5}{7}.\dfrac{9}{11}+1\dfrac{5}{7}\)
\(=\dfrac{-5}{7}.\left(\dfrac{2}{11}+\dfrac{9}{11}\right)+\dfrac{12}{17}\)
\(=\dfrac{-5}{7}.1+\dfrac{12}{7}\)
\(=\dfrac{-5}{7}+\dfrac{12}{7}\)
\(=1\)
c) \(11\dfrac{3}{13}-\left(2\dfrac{4}{7}+5\dfrac{3}{13}\right)\)
\(=11\dfrac{3}{13}-\dfrac{18}{7}-5\dfrac{3}{13}\)
\(=\left(11\dfrac{3}{13}-5\dfrac{3}{13}\right)-\dfrac{18}{7}\)
\(=6-\dfrac{18}{7}\)
\(=\dfrac{24}{7}\)
d) \(\dfrac{2}{7}.5\dfrac{1}{4}-\dfrac{2}{7}.3\dfrac{1}{4}\)
\(=\dfrac{2}{7}.\left(5\dfrac{1}{3}-3\dfrac{1}{4}\right)\)
\(=\dfrac{2}{7}.2\)
\(=\dfrac{4}{7}\)
Câu 2
a) \(\left(2x+7\right)+135=0\)
\(2x+7+135=0\)
\(2x+142=0\)
\(2x=-142\)
\(x=-\dfrac{142}{2}\)
\(x=-71\)
b) \(\dfrac{1}{2}x-\dfrac{2}{5}=\dfrac{1}{5}\)
\(\dfrac{1}{2}x=\dfrac{1}{5}+\dfrac{2}{5}\)
\(\dfrac{1}{2}x=\dfrac{3}{5}\)
\(x=\dfrac{3}{5}:\dfrac{1}{2}\)
\(x=\dfrac{6}{5}\)
c) \(10-\left|x+1\right|=5\)
\(\left|x+1\right|=10-5\)
\(\left|x+1\right|=5\)
\(x+1=5\); \(x+1=-5\)
*) \(x+1=5\)
\(x=5-1\)
\(x=4\)
*) \(x+1=-5\)
\(x=-5-1\)
\(x=-6\)
Vậy \(x=-6;x=4\)
d) \(\dfrac{1}{2}x+150\%x=2014\)
\(\dfrac{1}{2}x+\dfrac{3}{2}x=2014\)
\(2x=2014\)
\(x=\dfrac{2014}{2}\)
\(x=1007\)
