a) \(\left(19x+2\cdot5^2\right):14=\left(13-8\right)^2-4^2\)

\(\Leftrightarrow\left(19x+2\cdot25\right):14=5^2-4^2\)

\(\Leftrightarrow19x+50=\left(25-16\right)\cdot14\)

\(\Leftrightarrow19x+50=9\cdot14\)

\(\Leftrightarrow19x+50=126-50\)

\(\Leftrightarrow19x=76\)

\(\Leftrightarrow x=76:19\)

\(\Leftrightarrow x=4\)

b) \(x+\left(x+1\right)+\left(x+2\right)+...+\left(x+30\right)=1240\)

\(\Leftrightarrow\left(x+x+x+x...+x\right)+\left(1+2+3+...+30\right)=1240\)

\(\Leftrightarrow31x+\frac{\left[\left(30-1\right):1+1\right]\cdot\left(30+1\right)}{2}=1240\)

\(\Leftrightarrow31x+465=1240\)

\(\Leftrightarrow31x=775\)

\(\Leftrightarrow x=25\)

c)\(11-\left(-53+x\right)=97\)

\(\Leftrightarrow-53+x=-86\)

\(\Leftrightarrow x=-33\)

d) \(-\left(x+84\right)+213=-16\)

\(\Leftrightarrow-\left(x+84\right)=-229\)

\(\Leftrightarrow x+84=229\)

\(\Leftrightarrow x=145\)

a, (19x+2.5²) : 14 = (13-8)² - 4²

(19x + 2.25) : 14 = 5² - 4²

(19x + 50) : 14 = 25 - 16

(19x + 50) : 14 = 9

19 x + 50 = 9.14

19x + 50 = 126 

19x = 126 - 50

19x = 76

x = 76 : 19

x = 4

vậy____

b) x + (x + 1) + (x + 2) + (x + 3)+.....+(x+30) = 1240

(x+x+x+...+x) + (1+2+3+...+30) = 1240

31x + 465 = 1240

31x = 1240 - 465

31x = 775

x = 775 : 31

x = 25

vậy____

c) |x + 7| = 20 + 5.(-3)

|x + 7| = 20 + (-15)

|x + 7| = 5

\(\Rightarrow\orbr{\begin{cases}x+7=5\\x+7=-5\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=5-7\\x=-5-7\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=-2\\x=-12\end{cases}}\)

vậy_____

\(a,\left(19x+2.5^2\right):14=\left(13-8\right)^2-4^2\)

\(\Leftrightarrow\left(19x+50\right):14=5^2-4^2\)

\(\Leftrightarrow\left(19x+50\right):14=9\)

\(\Leftrightarrow19x+50=126\)

\(\Leftrightarrow19x=76\Leftrightarrow x=4\)

b) x + ( x + 1 ) + ( x + 2 ) + ... + ( x + 30 ) = 1240

x + x + 1 + x + 2 + ... + x + 30 = 1240

( x + x + ... + x ) + ( 1 + 2 + ... + 30 ) = 1240

Số số hạng là : ( 30 - 1 ) : 1 + 1 = 30 ( số )

Tổng là : ( 30 + 1 ) . 30 : 2 = 465

=> 31x + 465 = 1240

=> 31x = 775

=> x = 25

Vậy........

c) 11 - ( -53 + x ) = 97

11 + 53 - x = 97

64 - x = 97

x = 64 - 97

x = -33

\(\left(19x+2.5^2\right):14=\left(13-8\right)^2-4^2\)

\(\Rightarrow\left(19x+50\right):14=25-16\)

\(\Rightarrow19x+50=9.14=126\)

\(\Rightarrow19x=76\)

\(\Rightarrow x=76:19=4\)

(19x+2.5²):14 =(13-8)²-4²

(19x + 50):14  = 5²-4²

(19x + 50):14  = 9

19x + 50          = 9.14

 19x+50           = 126

  19x                 =76

     x                   =76:19

     x                   =4

Chúc các bn học tốt ah🥰🥰

     \(\frac{2}{\left(x+2\right)\left(x+4\right)}+\frac{4}{\left(x+4\right)\left(x+8\right)}+\frac{6}{\left(x+8\right)\left(x+14\right)}=\frac{x}{\left(x+2\right)\left(x+14\right)}\)

\(\Leftrightarrow\frac{x}{\left(x+2\right)\left(x+14\right)}=\frac{1}{x+2}-\frac{1}{x+4}+\frac{1}{x+4}-\frac{1}{x+8}-\frac{1}{x+8}-\frac{1}{x+14}\)

\(\Leftrightarrow\frac{x}{\left(x+2\right)\left(x+14\right)}=\frac{1}{x+2}-\frac{1}{x+14}\)

\(\Leftrightarrow\frac{x}{\left(x+2\right)\left(x+14\right)}=\frac{\left(x+14\right)-\left(x+2\right)}{\left(x+2\right)\left(x+14\right)}\)

\(\Leftrightarrow x=\left(x+14\right)-\left(x+2\right)\)

\(\Leftrightarrow x=x+14-x-2\)

\(\Leftrightarrow x=\left(x-x\right)+\left(14-2\right)\)

\(\Leftrightarrow x=0+12\)

\(\Leftrightarrow x=12\)

x=12

Áp dụng tổng đặc biệt đấy

\(\frac{2}{\left(x+2\right)\left(x+4\right)}+\frac{4}{\left(x+4\right)\left(x+8\right)}+\frac{6}{\left(x+8\right)\left(x+14\right)}=\frac{x}{\left(x+2\right)\left(x+14\right)}\)

\(\frac{1}{x+2}-\frac{1}{x+4}+\frac{1}{x+4}-\frac{1}{x+8}+\frac{1}{x+8}-\frac{1}{x+14}=\frac{x}{\left(x+2\right)\left(x+14\right)}\)

\(\frac{1}{x+2}-\frac{1}{x+14}=\frac{x}{\left(x+2\right)\left(x+14\right)}\)

\(\frac{12}{\left(x+2\right)\left(x+14\right)}=\frac{x}{\left(x+2\right)\left(x+14\right)}\)

\(\Rightarrow x=12\)