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( x + 1 ) + ( x + 4 ) + ( x + 7 ) + ... + ( x + 1996 ) = 666999
x + 1 + x + 4 + x + 7 + ... + x + 1996 = 666999
( x + x + x + ... + x ) + ( 1 + 4 +7 + ... + 1996 ) = 666999
666x + ( 1996 + 1 ) . 666 : 2 = 666999
666x + 665001 = 666999
666x = 1998
x = 3
(x+1)+(x+4)+(x+7)+...+(x+1996)=666999
x+1+x+4+x+7+...+x+1996=666999
(x+x+x+...+x)+(1+4+7+...+1996)=666999
Ta thấy : Số hạng thứ 2 là tổng của dãy số: 1+4+7+...+1996
Khoảng cách giữa 2 số liên tiếp là: 4-1=3
Số số hạng của dãy số trên là: (1996-1):3+1=666( sô hạng)
Số hạng thứ 2 là: (1996+1)x666:2= 665001
Ta có:
(x+x+x+...+x)+(1+4+7+...+1996)=666999
666x+665001=666999
666x=666999-665001
666x=1998
x=1998:666
x=3
=> x=3
( x +1 ) + ( x + 2 ) + ...+ ( x + 10) +...+ (x+ 1996 ) = (x+x+...+x) + (1+2+...+1996) (1996 số x)
= x.1996 + \(\frac{1996.1997}{2}\)= x.1996 + 1993006 = 666999 => x.1996 = 666999- 1993006 = -1326007
=> x = -1326007:1996 = -664.3321643
a)=> 3x-6+17=2x+16
=>3x-2x=16-17+6=5
=>x=5
b) => x+1+x+4+x+7+...+x+1996=666999
Số số hạng của dãy 1,4,7,...,1996 là
(1996-1):3+1=666
Tổng của dãy số 1,4,7,...,1996 là
(1996+1).666:2=665001
=> 666x+665001=666999
=>666x=666999-665001=1998
=>x=1998:666=3
Chọn mình nha . Chúc bạn học tốt . cảm ơn
\(1,\\ x+\dfrac{1}{2}=-\dfrac{5}{3}\\ x=-\dfrac{5}{3}-\dfrac{1}{2}\\ x=-\dfrac{13}{6}\\ Vậyx=-\dfrac{13}{6}\)
\(2,\\ \dfrac{1}{3}-x=\dfrac{3}{5}\\ x=\dfrac{1}{3}-\dfrac{3}{5}\\ x=-\dfrac{4}{15}\\ Vậyx=-\dfrac{4}{15}\)
\(3,\\ 3-4+x=\dfrac{7}{2}\\ -1+x=\dfrac{7}{2}\\ x=\dfrac{7}{2}+1\\ x=\dfrac{9}{2}\\ Vậyx=\dfrac{9}{2}\)
\(4,\\ x-\dfrac{4}{3}=-\dfrac{7}{9}\\ x=-\dfrac{7}{9}+\dfrac{4}{3}\\ x=\dfrac{15}{27}\\ Vậyx=\dfrac{15}{27}\)
\(5,\\ x-\left(-\dfrac{7}{3}\right)=\dfrac{5}{6}\\ x=\dfrac{5}{6}-\dfrac{7}{3}\\ x=-\dfrac{27}{18}\\ Vậyx=-\dfrac{27}{18}\)
\(6,\\ x-\dfrac{1}{5}=\dfrac{9}{10}\\ x=\dfrac{9}{10}+\dfrac{1}{5}\\ x=\dfrac{11}{10}\\ Vậyx=\dfrac{11}{10}\)
\(7,\\ x+\dfrac{5}{12}=\dfrac{3}{8}\\ x=\dfrac{3}{8}-\dfrac{5}{12}\\ x=-\dfrac{1}{24}\\ Vậyx=-\dfrac{1}{24}\)
\(8,\\ x+\dfrac{5}{4}=\dfrac{7}{6}\\ x=\dfrac{7}{6}-\dfrac{5}{4}\\ x=-\dfrac{9}{24}\\ Vậyx=-\dfrac{9}{24}\)
\(9,\\ x-\dfrac{2}{7}=\dfrac{1}{35}\\ x=\dfrac{1}{35}+\dfrac{2}{7}\\ x=\dfrac{11}{35}\\ Vậyx=\dfrac{11}{35}\\ 10,\\ x-\dfrac{1}{5}=-\dfrac{7}{10}\\ x=-\dfrac{7}{10}+\dfrac{1}{5}\\ x=-\dfrac{1}{2}\\ Vậyx=-\dfrac{1}{2}\)
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1/ \(x+\dfrac{1}{2}=\dfrac{-5}{3}\)
\(x=\dfrac{-5}{3}-\dfrac{1}{2}\)
\(x=\dfrac{-10}{6}-\dfrac{3}{6}\)
Vậy \(x=\dfrac{-13}{6}\)
2/\(\dfrac{1}{3}-x=\dfrac{3}{5}\)
\(-x=\dfrac{3}{5}-\dfrac{1}{3}\)
\(-x=\dfrac{9}{15}-\dfrac{5}{15}\)
\(-x=\dfrac{4}{15}\)
Vậy \(x=\dfrac{-4}{15}\)
3/ \(3-4+x=\dfrac{7}{2}\)
\(-4+x=\dfrac{7}{2}-3\)
\(-4+x=\dfrac{7}{2}-\dfrac{6}{2}\)
\(-4+x=\dfrac{1}{2}\)
\(x=\dfrac{1}{2}+4\)
\(x=\dfrac{1}{2}+\dfrac{8}{2}\)
Vậy \(x=\dfrac{9}{2}\)
4/ \(x-\dfrac{4}{3}=\dfrac{-7}{9}\)
\(x=\dfrac{-7}{9}+\dfrac{4}{3}\)
\(x=\dfrac{-7}{9}+\dfrac{12}{9}\)
Vậy \(x=\dfrac{5}{9}\)
5/ \(x-\dfrac{-7}{2}=\dfrac{5}{6}\)
\(x=\dfrac{5}{6}-\dfrac{7}{2}\)
\(x=\dfrac{5}{6}-\dfrac{21}{6}\)
Vậy \(x=\dfrac{-16}{6}=\dfrac{-8}{3}\)
6/ \(x-\dfrac{1}{5}=\dfrac{9}{10}\)
\(x=\dfrac{9}{10}+\dfrac{1}{5}\)
\(x=\dfrac{9}{10}+\dfrac{2}{10}\)
Vậy \(x=\dfrac{11}{10}\)
7/ \(x+\dfrac{5}{12}=\dfrac{3}{8}\)
\(x=\dfrac{3}{8}-\dfrac{5}{12}\)
\(x=\dfrac{9}{24}-\dfrac{10}{24}\)
Vậy \(x=\dfrac{-1}{24}\)
8/ \(x+\dfrac{5}{4}=\dfrac{7}{6}\)
\(x=\dfrac{7}{6}-\dfrac{5}{4}\)
\(x=\dfrac{14}{12}-\dfrac{15}{12}\)
Vậy \(x=\dfrac{-1}{12}\)
9/ \(x-\dfrac{2}{7}=\dfrac{1}{35}\)
\(x=\dfrac{1}{35}+\dfrac{2}{7}\)
\(x=\dfrac{1}{35}+\dfrac{10}{35}\)
Vậy \(x=\dfrac{11}{35}\)
10 /\(x-\dfrac{1}{5}=\dfrac{-7}{10}\)
\(x=\dfrac{-7}{10}+\dfrac{1}{5}\)
\(x=\dfrac{-7}{10}+\dfrac{2}{10}\)
Vậy \(x=\dfrac{-5}{10}=\dfrac{-1}{2}\)
\(\frac{x}{1\cdot4}+\frac{x}{4\cdot7}+\frac{x}{7\cdot10}+\frac{x}{10\cdot13}+\frac{x}{13\cdot16}=\frac{5}{2}\)
\(\Rightarrow\frac{x}{3}\left[\frac{3}{1\cdot4}+\frac{3}{4\cdot7}+\frac{3}{7\cdot10}+\frac{3}{10\cdot13}+\frac{3}{13\cdot16}\right]=\frac{5}{2}\)
\(\Rightarrow\frac{x}{3}\left[1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{16}\right]=\frac{5}{2}\)
\(\Rightarrow\frac{x}{3}\left[1-\frac{1}{16}\right]=\frac{5}{2}\)
\(\Rightarrow\frac{x}{3}\cdot\frac{15}{16}=\frac{5}{2}\)
\(\Rightarrow\frac{x}{3}=\frac{5}{2}:\frac{15}{16}\)
\(\Rightarrow\frac{x}{3}=\frac{5}{2}\cdot\frac{16}{15}\)
\(\Rightarrow\frac{x}{3}=\frac{1}{1}\cdot\frac{8}{3}\)
\(\Rightarrow\frac{x}{3}=\frac{8}{3}\Leftrightarrow x=8\)
2. \(7\left(-3\right)-5\left(3-x\right)=11-5\)
\(\Leftrightarrow-21-5\left(3-x\right)=6\)
\(\Leftrightarrow-5\left(3-x\right)=27\)
\(\Leftrightarrow3-x=-\frac{27}{5}\)
\(\Leftrightarrow x=-\frac{42}{5}\)
Vậy \(x=-\frac{42}{5}\)
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