Bài 1

S₂ = 21 + 23 + 25 + ... + 1001

Số số hạng của S₂:

(1001 - 21) : 2 + 1 = 491

⇒ S₂  = (1001 + 21) . 491 : 2 = 250901

--------

S₄  = 15 + 25 + 35 + ... + 115

Số số hạng của S₄:

(115 - 15) : 10 + 1 = 11

⇒ S₄ = (115 + 15) . 11 : 2 = 715

Bài 2

a) 2x - 138 = 2³.3²

2x - 138 = 8.9

2x - 138 = 72

2x = 72 + 138

2x = 210

x = 210 : 2

x = 105

b) 5.(x + 35) = 515

x + 35 = 515 : 5

x + 35 = 103

x = 103 - 35

x = 78

c) 814 - (x - 305) = 712

x - 305 = 814 - 712

x - 305 = 102

x = 102 + 305

x = 407

d) 20 - [7.(x - 3) + 4] = 2

7(x - 3) + 4 = 20 - 2

7(x - 3) + 4 = 18

7(x - 3) = 18 - 4

7(x - 3) = 14

x - 3 = 14 : 7

x - 3 = 2

x = 2 + 3

x = 5

e) 9ˣ⁻¹ = 9

x - 1 = 1

x = 1 + 1

x = 2

a) x = 2

b) x = 7.

c) x = 12

d) x = 45

e) x = 18.

f) x  = 10

a) x = 2.               

b) x = 7.

c) x= 12.

d)  x= 45.

e) x = 18.

f) x  = 10.

Hơi dài nên mình ko làm 

a) 35.(x-10)=35

         x-10= 35:35

         x-10= 1

             x= 1+10

            x= 10

b) 21.(32-x) =21

          32-x = 21:21

          32-x = 1

               x= 32-1

                x= 31

a)(x-15)=0     

x=15

Vậy c=15

b)(x-10)=1

x=11

Vậy x=11

`@` `\text {Ans}`

`\downarrow`

`A)`

`37 \times 46+37 \times 51+111`

`= 37 \times (46+51)+111`

`= 37 \times 97+111`

`= 3589 +111`

`= 3700`

`B)`

`35 \times 215-35 \times 210-175`

`= 35 \times (215-210)-175`

`= 35 \times 5-175`

`= 175-175=0`

`E)`

`76 \times 102-76 \times 2`

`= 76 \times (102-2)`

`= 76 \times 100`

`= 7600`

`C)`

`85 \times 94+85 \times 2 +170 \times 2`

`= 85 \times (94+2) + 170 \times 2`

`= 85 \times 96+170 \times 2`

`= 8160+340`

`= 8500`

`48 \times 56+28 \times 104`

`= 48 \times 28 \times 2+28 \times 104`

`= 28 \times (48 \times 2+104)`

`= 28 \times (96+104)`

`= 28 \times 200`

`= 5600`

`G)`

`206 \times 12-206-206`

`= 206 \times (12-1-1)`

`= 206 \times 10`

`= 2060`

a) 37 x 46 + 37 x 51 + 111

= 37 x ( 46 + 51 ) + 111

= 37 x 97 + 111

= 3589 + 111

= 3700

b) 35 x 215 - 35 x 210 - 175

= 35 x ( 215 - 210 ) - 175

= 35 x 5 - 175

= 175 - 175

= 0

e) 76 x 102 - 76 x 2

= 76 x ( 102 - 2 )

= 76 x 100

= 7600

c) 85 x 94 + 95 x 2 + 170 x 2

= 7990 + 2 x ( 95 + 170 )

= 7990 + 2 x 265

= 7990 + 530

= 8520

48 x 56 + 28 x 104

= 2688 + 2912

= 5600

g) 206 x 12 - 206 - 206

= 2472 - 206 - 206

= 2266 - 206

= 2060

Lời giải:

a.

$23+x=15$

$x=15-23=-8$

b.

$x-18=-23$

$x=-23+18=-5$

c.

$x+(-4)=16$

$x=16-(-4)=16+4=20$

d.

$25-x=-16$

$x=25-(-16)=25+16=41$

e.

$(-35)x=-210$

$x=(-210):(-35)=6$
f.

$(-2)(15-x)=60$

$15-x=60:(-2)=-30$
$x=15-(-30)=15+30=45$

a: \(\dfrac{1}{3}+\dfrac{3}{35}< \dfrac{x}{210}< \dfrac{4}{7}+\dfrac{3}{5}+\dfrac{1}{2}\)

\(\Leftrightarrow\dfrac{70}{210}+\dfrac{18}{210}< \dfrac{x}{210}< \dfrac{120}{210}+\dfrac{126}{210}+\dfrac{105}{210}\)

\(\Leftrightarrow88< x< 441\)

b: Ta có: \(\dfrac{5}{3}+\dfrac{-14}{3}< x< \dfrac{8}{5}+\dfrac{18}{10}\)

\(\Leftrightarrow\dfrac{5}{3}-\dfrac{14}{3}< x< \dfrac{8}{5}+\dfrac{9}{5}\)

=>-9/3<x<17/5

=>-3<x<3,4

mà x là số nguyên

nên \(x\in\left\{-2;-1;0;1;2;3\right\}\)

Bài 1:

a: \(250:\left\lbrack27+2^{10}:2^9-300:\left(74+1^5\right)\right\rbrack\)

\(=250:\left\lbrack27+2-300:\left(74+1\right)\right\rbrack\)

=250:(29-300:75)

=250:(29-4)

=250:25

=10

b: \(72+35:\left(-5\right)-4\cdot13\)

=72-52-35:5

=20-7

=13

Bài 2:

a: \(\left(x-5\right):41=7^{18}:\left(7^5\cdot7^{12}\right)\)

=>\(\left(x-5\right):41=7^{18}:7^{17}=7\)

=>\(x-5=41\cdot7=287\)

=>x=287+5

=>x=292

b: \(x-12x=5^1-115\)

=>-11x=5-115=-110

=>11x=110

=>x=110/11=10