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![](https://rs.olm.vn/images/avt/0.png?1311)
1, 2x - 35 = 15
2x = 15 + 35
2x = 50
x = 50 : 2
x = 25.
2, 3x + 18 = 12
3x = 12 - 18
3x = -6
x = -6 : 3
x = -2.
3, / x - 1 / = 0
=> x \(\in\varnothing\).
4, -13 /x/ = - 26
/x/ = -26 : -13
=> \(\orbr{\begin{cases}x=2\\x=-2\end{cases}}\)
Vậy x \(\in\){ 2 ; -2}.
5,4 - ( 27 - 3 ) = x - ( 13 - 4 )
4 - 24 = x - 9
-20 = x - 9
-x = 9 + 20
-x = 29
x = -29.
6, 47 - ( x + 15 ) = 21
47 - x - 15 = 21
-x - 15 = 21 - 47
-x - 15 = -26
-x = -26 + 15
-x = - 11
x = 11.
7, -5 -( 24 - x) = - 11
-5 - 24 + x = -11
-24 + x = -11 + 5
-24 + x = -6
x = -6 + 24
x = 18.
8, 6 - /x/ = 2
/x/ = 6 - 2
\(\orbr{\begin{cases}x=3\\x=-3\end{cases}}\)
Vậy x \(\in\left\{3;-3\right\}.\)
9, 6 + /x/ = 2
/x/ = 2 - 6
=> x = -4.
2x - 35 = 15
=> 2x = 15 + 35
=> x = 50 : 2
=> x = 25
3x + 18 = 12
=> 3x = 12 - 18
=> x = ( -6 ) : 3
=> x = -2
| x - 1 | = 0
=> x - 1 = 0
=> x = 0 + 1
=> x = 1
-13 * | x | = -26
=> | x | = -26 : ( -13 )
=> | x | = 2
![](https://rs.olm.vn/images/avt/0.png?1311)
a) (x - 1) + (x + 2) + (x - 3) + (x + 4) + (x - 5) + (x + 6) = 21
x - 1 + x + 2 + x - 3 + x + 4 + x - 5 + x + 6 = 21
6x + 3 = 21
6x = 21 - 3
6x = 18
x = 18 : 6
x = 3
b) (x - 1) + (x + 3) + (x - 5) + (x + 7) + (x - 9) + (x + 11) = 186
x - 1 + x + 3 + x - 5 + x + 7 + x - 9 + x + 11 = 186
6x + 6 = 186
6x = 186 - 6
6x = 180
x = 180 : 6
x = 30
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:
A = 1 + 3 + 5 + 7 +... + 101
A = \(\frac{102.51}{2}=2601\)
M = 16 - 18 + 20 - 22 + 24 - 26 + .. + 64 - 66 + 68
M = ( 16 - 18 ) + ( 20 - 22 ) + ( 24 - 26 ) + ... + ( 64 - 66 ) + 68
M = (- 2 + - 2 + -2 + ... + - 2 ) + 68
M = 25/2 . ( - 2 ) + 68
M = -25 + 68
M = 43
H = ( 1 + 2 + 3 +...+ 99 ) x ( 13 x 15 - 12 x 15 - 15 )
H = ( 1 + 2 + 3 +...+ 99 ) x { (13 - 12 - 1) x 15 }
H = ( 1 + 2 + 3 +...+ 99 ) x 0
H = 0
G = 1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + 9 + 10 - 11 - 12 + 13 + 14 - ... + 301 + 302
G = ( 1 + 2 ) + ( -3 - 4 ) + ( 5 + 6 ) + ( -7 - 8 ) + ( 9 + 10 ) + ( - 11 - 12 ) + ( 13 + 14 ) -...+ ( 301 + 302 )
G = ( 3 - 7 ) + ( 11 - 15 ) + ( 19 - 23 ) + 27 - ... + 603
G = -4 + - 4 + -4 + 27 - ... + 603
G = 75 x ( -4 ) + 603
G = -300 + 603
G = 303
2.
a) 1 + 2 + 3 + 4 +...+ 99 + 100 + 2 x X = 5052
= > \(\frac{100.101}{2}\)+ 2 x X = 5052
= > 5050 + 2 x X = 5052
= > 2X = 2
= > X = 1
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(\left(\frac{1}{3}+\frac{1}{5}\right)+\left(\frac{1}{6}-\frac{1}{5}\right)=\left(\frac{1}{3}+\frac{1}{6}\right)+\left(\frac{1}{5}-\frac{1}{5}\right)=\frac{1}{2}\)
b) \(\frac{3}{16}\times\frac{7}{5}+\frac{3}{5}\times\frac{9}{16}=\frac{21}{80}+\frac{27}{80}=\frac{48}{80}=\frac{3}{5}\)
c) \(\frac{1}{1\times2}+\frac{1}{2\times3}+...+\frac{1}{2020\times2021}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2020}-\frac{1}{2021}\)
\(=1-\frac{1}{2021}=\frac{2020}{2021}\)
d) \(\frac{1}{1\times3}+\frac{1}{3\times5}+...+\frac{1}{2021\times2023}=\frac{1}{2}\times\left(\frac{2}{1\times3}+\frac{2}{3\times5}+...+\frac{2}{2021\times2023}\right)\)
\(=\frac{1}{2}\times\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2021}-\frac{1}{2023}\right)\)
\(=\frac{1}{2}\times\left(1-\frac{1}{2023}\right)=\frac{1}{2}\times\frac{2022}{2023}=\frac{1011}{2023}\)
e) \(\frac{3}{2}\times\frac{1}{7}\times\frac{5}{4}+\frac{15}{2}\times\frac{6}{7}\times\frac{1}{4}==\frac{15}{56}+\frac{80}{56}=\frac{95}{56}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a, 53 x 39 + 47 x 39 + 53 x 21- 47 x 21
= ( 53 + 47 ) x 39 + ( 53 - 47 ) x 21
= 100 x 39 + 6 x 21
= 3900 + 126
= 4026
Mấy phần khác bạn tự làm đi
![](https://rs.olm.vn/images/avt/0.png?1311)
123,45 + 23,56 +76,44 + 54,55
= (123,45 + 54,55) + (23,56 + 76,44)
= 178 + 100
= 278
456 x 45 + 456 x 10 + - 456 x 55
=456 x (45 +10-55)
=456 x 0
=0
2,5 x 8,5 + 7,5 x 8,5
=8,5 x (2,5 +7,5)
= 8,5 x 10
= 85
86 x 5 + 86 x 4 + 86
= 86 x (5+4+1)
= 86 x10
860
a)=1/3-1/7+1/7-1/11+1/11-1/15+...+1/107-1/111
=1/3-1/111
a) Ta có: \(G=\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+...+\frac{4}{107.111}\)
\(=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...+\frac{1}{17}-\frac{1}{111}\)
\(=\frac{1}{3}-\frac{1}{111}\)
\(=\frac{12}{37}\)
Vậy \(G=\frac{12}{37}\)