(x+3)+(x+6)+...+(x+51)=493

=>17x+(3+6+...+51)=493

=>\(17x+3\left(1+2+...+17\right)=493\)

=>\(17x+3\cdot17\cdot\dfrac{18}{2}=493\)

=>\(17x+51\cdot9=493\)

=>17x=34

=>x=2

(x+2)+(x+4)+...+(x+20)=260

=>10x+(2+4+...+20)=260

=>\(10x+2\left(1+2+...+10\right)=260\)

=>\(10x+2\cdot10\cdot\dfrac{11}{2}=260\)

=>\(10x+110=260\)

=>10x=150

=>\(x=\dfrac{150}{10}=15\)

Số nhóm trong phép tỉnh tổng trên là: 

`(20 - 2) : 2 + 1 = 10` (nhóm)

`(x + 2) + (x+4) + ... + (x+20) = 260`

`=> 10x + (2+4+...+20) = 260`

`=> 10x + (20+2) . 10 = 260`

`=> 10x + 22. 10 = 260`

`=> 10x + 220 = 260`

`=> 10x = 260 - 220`

`=> 10x = 40`

`=> x = 40 : 10`

`=> x = 4`

Vậy `x = 4`

\(2n-1⋮2n+3\)

=>\(2n+3-4⋮2n+3\)

=>\(-4⋮2n+3\)

=>\(2n+3\in\left\{1;-1;2;-2;4;-4\right\}\)

=>\(2n\in\left\{-2;-4;-1;-5;1;-7\right\}\)

=>\(n\in\left\{-1;-2;-\dfrac{1}{2};-\dfrac{5}{2};\dfrac{1}{2};-\dfrac{7}{2}\right\}\)

\(2n+1⋮n+5\)

=>\(2n+10-9⋮n+5\)

=>\(-9⋮n+5\)

=>\(n+5\in\left\{1;-1;3;-3;9;-9\right\}\)

=>\(n\in\left\{-4;-6;-2;-8;4;-14\right\}\)

\(372-19\cdot4+981:19-13\)

=372-76+981/19-13

\(=283+\dfrac{981}{19}=\dfrac{6358}{19}\)

Bạn làm 2 Trg họp thôi
x- 15= 0 x =15
2x-16=0 x=8

ta có 2 trương hợp

th1 x-15 =0

x=0+15

x=15

th2

2x-16=0

2x=16

x=8

a: \(x+40\%\cdot x=5\)

=>\(x\left(1+0,4\right)=5\)

=>1,4x=5

=>\(x=\dfrac{5}{1,4}=\dfrac{50}{14}=\dfrac{25}{7}\)

b: \(1,2x-80\%x=\dfrac{1}{4}\)

=>1,2x-0,8x=0,25

=>0,4x=0,25

=>\(x=\dfrac{0.25}{0.4}=\dfrac{25}{40}=\dfrac{5}{8}\)

d: \(x\cdot x-\dfrac{1}{9}=\dfrac{1}{3}\)

=>\(x^2=\dfrac{1}{9}+\dfrac{1}{3}=\dfrac{4}{9}\)

=>\(\left[{}\begin{matrix}x=\dfrac{2}{3}\\x=-\dfrac{2}{3}\end{matrix}\right.\)

2x-31=4646:46

=>2x-31=101

=>2x=31+101=132

=>\(x=\dfrac{132}{2}=66\)

12+40:(17-x)=52

=>40:(17-x)=40

=>17-x=40:40=1

=>x=17-1=16

40:( 17-x)=40

17-x=40: 40

17-x=1

x=17-1

x=16

\(3n+22⋮2n+3\)

=>\(6n+44⋮2n+3\)

=>\(6n+9+35⋮2n+3\)

=>\(35⋮2n+3\)

mà 2n+3>=3(Vì n là số tự nhiên)

nên \(2n+3\in\left\{5;7;35\right\}\)

=>\(n\in\left\{1;2;16\right\}\)

\(16\left(143-x\right)-2\left(143-x\right)=1414\)

=>\(14\left(143-x\right)=1414\)

=>143-x=1414:14=101

=>x=143-101=42

16 x (143 - \(x\)) - 2 x (143 - \(x\)) = 1414

        (143 - \(x\)) x (16 - 2) = 1414

       (143 - \(x\)) x 14 = 1414

        143 - \(x\)          = 1414 : 14

        143 - \(x\)         = 101

                 \(x\)         = 143 - 101

                 \(x\)         = 42

              Vậy \(x=42\)