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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) \(-\left(x+84\right)+213=-16\)
\(\Leftrightarrow-\left(x+84\right)=-229\)
\(\Leftrightarrow x+84=229\)
\(\Leftrightarrow x=145\)
\(a,\left(19x+2.5^2\right):14=\left(13-8\right)^2-4^2\)
\(\Leftrightarrow\left(19x+50\right):14=5^2-4^2\)
\(\Leftrightarrow\left(19x+50\right):14=9\)
\(\Leftrightarrow19x+50=126\)
\(\Leftrightarrow19x=76\Leftrightarrow x=4\)
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........
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_____
\(\left(19x+2.5^2\right):14=\left(13-8\right)^2-4^2\)
\(\Rightarrow\left(19x+50\right):14=25-16\)
\(\Rightarrow19x+50=9.14=126\)
\(\Rightarrow19x=76\)
\(\Rightarrow x=76:19=4\)
a/
\(VT=\dfrac{\left(x+4\right)-\left(x+2\right)}{\left(x+2\right)\left(x+4\right)}+\dfrac{\left(x+8\right)-\left(x+4\right)}{\left(x+4\right)\left(x+8\right)}+\dfrac{\left(x+14\right)-\left(x+8\right)}{\left(x+8\right)\left(x+14\right)}=\)
\(=\dfrac{1}{x+2}-\dfrac{1}{x+4}+\dfrac{1}{x+4}-\dfrac{1}{x+8}+\dfrac{1}{x+8}-\dfrac{1}{x+14}=\)
\(=\dfrac{1}{x+2}-\dfrac{1}{x+14}=\dfrac{12}{\left(x+2\right)\left(x+14\right)}\)
\(\Rightarrow\dfrac{12}{\left(x+2\right)\left(x+14\right)}=\dfrac{x}{\left(x+2\right)\left(x+14\right)}\left(x\ne-2;x\ne-14\right)\)
\(\Rightarrow x=12\)
\(\dfrac{x}{2023}+\dfrac{x+1}{2022}+...+\dfrac{x+2022}{1}+2023=0\)
\(\dfrac{1}{2023}x+\dfrac{1}{2022}x+\dfrac{1}{2022}\cdot1+...+\dfrac{1}{1}x+\dfrac{1}{1}\cdot2022+2023=0\)
\(x\left(\dfrac{1}{2023}+\dfrac{1}{2022}+...+\dfrac{1}{1}\right)+\left(\dfrac{1}{2022}+\dfrac{2}{2021}+...+\dfrac{2022}{1}+2023\right)=0\)
\(x\left(\dfrac{1}{2023}+\dfrac{1}{2022}+...+\dfrac{1}{1}\right)=\dfrac{1}{2022}+\dfrac{2}{2021}+...+\dfrac{2022}{1}+2023\)
\(x=\dfrac{\dfrac{1}{2022}+\dfrac{2}{2021}+...+\dfrac{2022}{1}+2023}{\dfrac{1}{2023}+\dfrac{1}{2022}+...+\dfrac{1}{1}}\)
\(x=\dfrac{\dfrac{1}{2022}+\dfrac{2022}{2022}+\dfrac{2}{2021}+\dfrac{2021}{2021}+...+\dfrac{2022}{1}+\dfrac{1}{1}}{\dfrac{1}{2023}+\dfrac{1}{2022}+...+\dfrac{1}{1}}\)
\(x=\dfrac{\dfrac{2023}{2022}+\dfrac{2023}{2021}+...+\dfrac{2023}{1}}{\dfrac{1}{2022}+\dfrac{1}{2021}+...+\dfrac{1}{1}}=2023\)
Vậy x = 2023
