Giải:

Đặt \(A=\dfrac{6}{4.7}+\dfrac{6}{7.10}+\dfrac{6}{10.13}+...+\dfrac{6}{82.85}\)

\(\dfrac{1}{2}A=\dfrac{3}{4.7}+\dfrac{3}{7.10}+\dfrac{3}{10.13}+...+\dfrac{3}{82.85}\)

\(\dfrac{1}{2}A=\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{13}+...+\dfrac{1}{82}-\dfrac{1}{85}\)

\(\dfrac{1}{2}A=\dfrac{1}{4}-\dfrac{1}{85}\)

\(\dfrac{1}{2}A=\dfrac{81}{340}\)

\(\Rightarrow A=\dfrac{81}{340}:\dfrac{1}{2}\)

\(A=\dfrac{81}{170}\)

Bài 1: 

a: x+1/2=5/6

nên x=5/6-1/2=1/3

b: x+1/4=3/4

nên x=3/4-1/4=2/4=1/2

c: x+3/10=1/2

nên x=1/2-3/10=5/10-3/10=1/5

d: x+1/4=3/8

nên x=3/8-1/4=3/8-2/8=1/8

TOT LAM

a) \(39\times118+29\times82\)

\(=39\times2\times59+29\times2\times41\)

\(=2\times\left(39\times59+29\times41\right)\)

\(=2\times\left(2301+1189\right)\)

\(=2\times3490\)

\(=6980\)

b) \(37\times39+78\times14-13\times85-52\times55\)

\(=37\times3\times13+6\times13\times14+13\times85-4\times13\times55\)

\(=13\times\left(37\times3+6\times14+85-4\times55\right)\)

\(=13\times\left(111+84+85-220\right)\)

\(=13\times\left(280-220\right)\)

\(=13\times60\)

\(=780\)

c) \(368:16+752:16+480:16\)

\(=\left(368+752+480\right):16\)

\(=\left(1120+480\right):16\)

\(=1600:16\)

\(=100\)

d) \(5\times11\times18+9\times31\times10+4\times29\times45\)

\(=5\times11\times9\times2+9\times31\times10+2\times2\times29\times5\times9\)

\(=10\times9\times11+10\times9\times31+10\times29\times2\times9\)

\(=90\times11+90\times31+90\times29\times2\)

\(=90\times\left(11+31+29\times2\right)\)

\(=90\times\left(42+58\right)\)

\(=90\times100\)

\(=9000\)

a,\(7-\left(18+x\right)=-15\)

\(18+x=7-\left(-15\right)\)

\(18+x=22\)

\(x=4\)

b,\(\left(x-17\right)-\left(-3\right)=0\)

\(x-17=-3\)

\(x=14\)

c,\(-18-\left(x-6\right)=0\)

\(x-6=-18\)

\(x=-12\)

d,\(29-\left(10+29\right)=x-\left(27-9\right)\)

\(x-18=-10\)

\(x=8\)

a) \(7-\left(18+x\right)=-15\)

\(\Leftrightarrow18+x=7+15\)

\(\Leftrightarrow18+x=22\)

\(\Leftrightarrow x=22-18\)

\(\Leftrightarrow x=4\)

b) \(\left(x-17\right)-\left(-3\right)=0\)

\(\Leftrightarrow\left(x-17\right)+3=0\)

\(\Leftrightarrow x-17=0-3\)

\(\Leftrightarrow x-17=-3\)

\(\Leftrightarrow x=-3+17\)

\(\Leftrightarrow x=14\)

c) \(-18-\left(x-6\right)=0\)

\(\Leftrightarrow x-6=0+\left(-18\right)\)

\(\Leftrightarrow x-6=-18\)

\(\Leftrightarrow x=-18+6\)

\(\Leftrightarrow x=-12\)

d) \(29-\left(10+29\right)=x-\left(27-9\right)\)

\(\Leftrightarrow29-10-29=x-27+9\)

\(\Leftrightarrow-10=x-27+9\)

\(\Leftrightarrow x-27=-10-9\)

\(\Leftrightarrow x-27=-19\)

\(\Leftrightarrow x=-19+27\)

\(\Leftrightarrow x=8\)

a)
7 - (18 + x) = -15
18 + x = 7 - ( -15 )
18 + x = 7 + 15
18 + x = 22
x = 22 - 18
x = 4
b)
(x - 17) - (-3) = 0
x - 17 = 0 + -3
x - 17 = -3
x = -3 + 17
x = 14
c)
-18 - (x - 6) = 0
x - 6 = -18 - 0
x - 6 = -18
x = -18 + 6
x = -12
d)
29 - (10 + 29) = x - (27 - 9)
29 - 39 = x - 18
x - 18 = -10
x = -10 + 18
x = 8

1,7-(18+x)=-15

<=>18+x=7+15

<=>18+x=22

<=>x=4

2,(x-17)-(-3)=0

<=>x-17+3=0

<=>x-17=-3

,<=>x=14

<=>

1, 

7 - ( 18 + x ) = - 15 

18 + x = 7 + 15 

18 + x = 22

x = 22 - 18 

x = 4 

2,

( x - 17 ) - ( - 3 ) = 0 

( x - 17 ) + 3 = 0 

x - 17 = - 3 

x = -3 + 17 

x = 14 

3, -18 - ( x - 6 ) = 0 

-18 = x- 6 

x = - 18 + 6 

x = - 12 

4,   29 - ( 10 + 29 ) = x - ( 27 - 9 )

-10 = x - 18 

x = - 10 + 18 

x = 8

(11 / 29 + 2 / 29 + 16 / 29 ) . 9 / 10

1 . 9/10 = 9/10

\(\dfrac{9}{10}\times\left(\dfrac{11}{29}+\dfrac{2}{29}+\dfrac{16}{29}\right)=\dfrac{9}{10}\times\dfrac{29}{29}=\dfrac{9}{10}\times1=\dfrac{9}{10}\)

= 9/10 x ( 11/29 + 2/9 + 16/29 )

= 9/10 x 1

= 9/10