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Ta có : (-1)+3+(-5)+7+.....+[-(x-2)+x]=600
[(-1)+3]+[(-5)+7]+.....+[-(x-2)]+x=600
2 + 2 + .... + 2 = 600
2 . (1+1+ ...... + 1 ) = 600
\(\Leftrightarrow\) 1 + 1 + .... + 1 = 600 : 2
\(\Leftrightarrow\)1 + 1 + ..... + 1 = 300
Số dấu [] là : (x - 3 ) : 4 + 1
\(\Rightarrow\)(x - 3 ) : 4 + 1 = 300
\(\Rightarrow\)(x-3) : 4 = 299
\(\Rightarrow\)x - 3 = 299 x 4
\(\Rightarrow\)x - 3 = 1196
\(\Rightarrow\)x = 1196 + 3
\(\Rightarrow\)x = 1199
Vậy x = 1199.
# HOK TỐT #
\(35\cdot18-5\cdot7\cdot28\)
\(=35\cdot18-35\cdot28\)
\(=35\cdot\left(18-28\right)\)
\(=35\cdot\left(-10\right)\)
\(=-350\)
Ta có : \(\frac{5}{11}+\frac{5}{12}+\frac{5}{13}+\frac{5}{14}\)
\(=5.\left(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}\right)\)
\(< 5.\left(\frac{1}{11}+\frac{1}{11}+\frac{1}{11}+\frac{1}{11}\right)\)
\(=5.\frac{4}{11}\)
\(=\frac{20}{11}< \frac{20}{10}< 2\)
Vậy \(\frac{5}{11}+\frac{5}{12}+\frac{5}{13}+\frac{5}{14}< 2\left(đpcm\right)\)
a) Cách 1: \(\left(-8\right)\cdot\left(5+3\right)=\left(-8\right)\cdot8=-64.\)
Cách 2: \(\left(-8\right)\cdot\left(5+3\right)=\left(-8\right)\cdot5+\left(-8\right)\cdot3=-40-24=-64.\)
Hai kết quả như nhau.
b) Cách 1: \(\left(-3+3\right)\cdot\left(-5\right)=0\cdot\left(-5\right)=0\)
Cách 2: \(\left(-3+3\right)\cdot5=\left(-3\right)\cdot5+3\cdot5=-15+15=0\)
Hai kết quả như nhau.
\(a,\dfrac{7}{12}-\left(x+\dfrac{7}{10}\right):\dfrac{6}{5}=\dfrac{5}{4}\)
\(\Leftrightarrow\dfrac{7}{12}-x-\dfrac{7}{10}:\dfrac{6}{5}=\dfrac{5}{4}\)
\(\Leftrightarrow\dfrac{7}{12}-x-\dfrac{7}{12}=\dfrac{5}{4}\)
\(\Leftrightarrow\dfrac{7}{12}-x=\dfrac{5}{4}+\dfrac{7}{12}\)
\(\Leftrightarrow\dfrac{7}{12}-x=\dfrac{11}{6}\)
\(\Leftrightarrow x=\dfrac{7}{12}-\dfrac{11}{6}\)
\(\Leftrightarrow\dfrac{-5}{4}\)
Ta có : \(A=\frac{5}{3.9}+\frac{5}{9.15}+\frac{5}{5.21}+.....+\frac{5}{63.69}\)
\(\Rightarrow A=\frac{5}{6}\left(\frac{6}{3.9}+\frac{6}{9.15}+\frac{6}{15.21}+......+\frac{6}{63.69}\right)\)
\(\Rightarrow A=\frac{5}{6}\left(\frac{1}{3}-\frac{1}{9}+\frac{1}{9}-\frac{1}{15}+.....+\frac{1}{63}-\frac{1}{69}\right)\)
\(\Rightarrow A=\frac{5}{6}\left(\frac{1}{3}-\frac{1}{69}\right)\)
\(\Rightarrow A=\frac{5}{6}.\frac{22}{69}=\frac{55}{207}\)