6/4 x 19/10 - 3/4 x 7/1 + 3/4 : 10/69
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\(\frac{6}{4}\cdot\frac{19}{10}-\frac{3}{4}\cdot\frac{7}{10}+\frac{3}{4}:\frac{10}{69}=2^{ }_{ }\)\(\frac{15}{46}\)
vế 1 (6:4 =1.5 )x(19:10 =1.9)1,5x1,9 =2,85
vế 2 (3/4=0,75)x(7:10=0,7)0,75x0,7=0,525
vế 3 (3:4=0,75):(10:69=0,14492753623 lấy 3 chữ số ở hàng thập phân =0,144) 0,75:0,144=6,57894736842 lấy 3 chữ số ở hàng thập phân =6,578
2,85 -0,525+6,578
=2,325+6,578
=8.903
(hơi rườm rà nếu có sai thông cảm)
vế 1 6/4 x 19/10=57/20
vế 2 3/4 x 7/10=21/40
vế 3 3/4 : 10/69 =207/40
57/20 - 21/40 + 207/40
= 93/40 + 207/40
=15/2
X = ( 1+10 ) * 10 / 2 = 11 * 10 / 2 = 110 / 2 = 55
X= (2+20) * 10 /2 = 110
X= (1+19)*10/2= 100
1+2+3+4+5+6+7+8+9+10= (10+1)X10 : 2 = 55
2+4+6+8+10+12+14+16+18+20 = (20+2)x10 : 2 = 110
1+3+5+7+9+11+13+15+17+19 = (19+1) x 10 : 2 = 100
Câu 1 :
a, \(\frac{3\left(2x+1\right)}{4}-\frac{5x+3}{6}=\frac{2x-1}{3}-\frac{3-x}{4}\)
\(\Leftrightarrow\frac{6x+3}{4}+\frac{3-x}{4}=\frac{2x-1}{3}+\frac{5x+3}{6}\)
\(\Leftrightarrow\frac{5x+6}{4}=\frac{9x+1}{6}\Leftrightarrow\frac{30x+36}{24}=\frac{36x+4}{24}\)
Khử mẫu : \(30x+36=36x+4\Leftrightarrow-6x=-32\Leftrightarrow x=\frac{32}{6}=\frac{16}{3}\)
tương tự
\(\frac{19}{4}-\frac{2\left(3x-5\right)}{5}=\frac{3-2x}{10}-\frac{3x-1}{4}\)
\(< =>\frac{19.5}{20}-\frac{8\left(3x-5\right)}{20}=\frac{2\left(3-2x\right)}{20}-\frac{5\left(3x-1\right)}{20}\)
\(< =>95-24x+40=6-4x-15x+5\)
\(< =>-24x+135=-19x+11\)
\(< =>5x=135-11=124\)
\(< =>x=\frac{124}{5}\)
1/ Suy ra: -35 + 7x - 2x + 20 = 15
5x - 15 = 15
5x = 30
x = 6
2/ Suy ra: 4x - 20 - 3x - 21 = -19
x - 41 = -19
x = 22
3/ Suy ra: 8 - 4x + 3x - 15 = 14
-7 -x = 14
x = -7 -14
x = -21
4/ Suy ra: 7x - 63 - 30 + 5x = -6 + 11x
7x + 5x - 11x = -6 +63 + 30
x = 87
5/ Suy ra: -21x +35 + 14x - 28 = 28
-21x + 14x = 28 +28 - 35
-7x = 21
x= -3
6/ Suy ra: 20 - 5x + 7x - 14 = -2
2x = -8
x = -4
7/ Suy ra: 4x +15 -5x = 7
-x = -8
x = 8
8/ Suy ra: 5x - 35 +30 -10x = 20
-5x - 5 = 20
-5x = 25
x = -5
9/ Suy ra: 35 - 7x + 5x - 10 = 15
-7x + 5x = 15 +10 - 35
-2x = -10
x = 5
1) \(A=\frac{7}{10\times11}+\frac{7}{11\times12}+\frac{7}{12\times13}+...+\frac{7}{69\times70}\)
\(A=7\times\left(\frac{1}{10\times11}+\frac{1}{11\times12}+\frac{1}{12\times13}+...+\frac{1}{69\times70}\right)\)
\(A=7\times\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+...+\frac{1}{69}-\frac{1}{70}\right)\)
\(A=7\times\left(\frac{1}{10}-\frac{1}{70}\right)\)
\(A=7\times\frac{3}{35}\)
\(A=\frac{3}{5}\)
2) \(B=\frac{1}{25\times27}+\frac{1}{27\times29}+\frac{1}{29\times31}+...+\frac{1}{73\times75}\)
\(B=\frac{1}{2}\times\left(\frac{2}{25\times27}+\frac{2}{27\times29}+\frac{2}{29\times31}+...+\frac{2}{73\times75}\right)\).
\(B=\frac{1}{2}\times\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+\frac{1}{29}-\frac{1}{31}+...+\frac{1}{73}-\frac{1}{75}\right)\)
\(B=\frac{1}{2}\times\left(\frac{1}{25}-\frac{1}{75}\right)\)
\(B=\frac{1}{2}\times\frac{2}{75}\)
\(B=\frac{1}{75}\)
3) \(C=\frac{4}{2\times4}+\frac{4}{4\times6}+\frac{4}{6\times8}+...+\frac{4}{2008\times2010}\)
\(C=\frac{4}{2}\times\left(\frac{2}{2\times4}+\frac{2}{4\times6}+\frac{2}{6\times8}+...+\frac{2}{2008\times2010}\right)\)
\(C=2\times\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2008}-\frac{1}{2010}\right)\)
\(C=2\times\left(\frac{1}{2}-\frac{1}{2010}\right)\)
\(C=2\times\frac{502}{1005}\)
\(C=\frac{1004}{1005}\)
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