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1, \(\dfrac{x-1}{2009}+\dfrac{x-2}{2008}=\dfrac{x-3}{2007}+\dfrac{x-4}{2006}\)
\(\Leftrightarrow\left(\dfrac{x-1}{2009}-1\right)+\left(\dfrac{x-2}{2008}-1\right)=\left(\dfrac{x-3}{2007}-1\right)+\left(\dfrac{x-4}{2006}-1\right)\) ( Trừ mỗi vế cho 2 ta được phương trình như này nhé ! )
\(\Leftrightarrow\dfrac{x-2010}{2009}+\dfrac{x-2010}{2008}=\dfrac{x-2010}{2007}+\dfrac{x-2010}{2006}\)
\(\Leftrightarrow\dfrac{x-2010}{2009}+\dfrac{x-2010}{2008}-\dfrac{x-2010}{2007}-\dfrac{x-2010}{2006}=0\)
\(\Leftrightarrow\left(x-2010\right)\left(\dfrac{1}{2009}+\dfrac{1}{2008}-\dfrac{1}{2007}-\dfrac{1}{2006}\right)=0\)
Do \(\dfrac{1}{2009}+\dfrac{1}{2008}-\dfrac{1}{2007}-\dfrac{1}{2006}\ne0\) nên \(x-2010=0\Leftrightarrow x=2010\)
2, \(\dfrac{59-x}{41}+\dfrac{57-x}{43}+\dfrac{55-x}{45}+\dfrac{53-x}{47}+\dfrac{51-x}{49}=-5\)
\(\left(\dfrac{59-x}{41}+1\right)+\left(\dfrac{57-x}{43}+1\right)+\left(\dfrac{55-x}{45}+1\right)+\left(\dfrac{53-x}{47}+1\right)+\left(\dfrac{51-x}{49}+1\right)=0\)
\(\Leftrightarrow\dfrac{100-x}{41}+\dfrac{100-x}{43}+\dfrac{100-x}{45}+\dfrac{100-x}{47}+\dfrac{100-x}{49}=0\) \(\Leftrightarrow\left(100-x\right)\left(\dfrac{1}{41}+\dfrac{1}{43}+\dfrac{1}{45}+\dfrac{1}{47}+\dfrac{1}{49}\right)=0\) Do \(\dfrac{1}{41}+\dfrac{1}{43}+\dfrac{1}{45}+\dfrac{1}{47}+\dfrac{1}{49}\ne0\) nên \(100-x=0\Leftrightarrow x=100\)
Tìm x :
\(\dfrac{3}{7}\) . 5 - 9 = \(\dfrac{3\text{x}+57}{x}\) + 161\(\dfrac{1}{7}\)
\(\dfrac{15}{7}\) - 9 = \(\dfrac{3\text{x}}{x}\) + \(\dfrac{57}{x}\) + \(161\dfrac{1}{7}\)
\(\dfrac{15}{7}\) - 9 = 3 + 57 : x + 161\(\dfrac{1}{7}\)
\(\dfrac{-48}{7}\) = \(164\dfrac{1}{7}\) + 57 : x
=> 164\(\dfrac{1}{7}\) + 57 : x = \(\dfrac{-48}{7}\)
=> 57 : x = \(\dfrac{-48}{7}\) - 164\(\dfrac{1}{7}\)
=> 57 : x = -171
=> x = -171 . 57
=> x = -9747
Vậy : x = -9747
a. \(3\dfrac{1}{3}x+16=13,25\)
=> x + 16 = 13,25
=> x = 13,25 - 16
=> x = \(-\dfrac{11}{4}\)
b. x - 43 = (57 - x) - 50
=> 2x = 57 - 50 + 43
=> 2x = 7 + 43
=> 2x = 50
=> x = 50 : 2
=> x = 25
1)x - 26 =95 2)79 - x = 65 3)119 - x =97 4) (x - 67) -23 =10
x =95+26 x=79-65 x =119-97 x - 67 =10+23 =33
x =121 x=14 x =22 x =33+67
x =100
a, -x+28 = 34
=> -x = 34-28 =6
=> x= -6
b, -57-(11 - x ) =8
=> 11 - x = -57-8 = -65
=> x= 11 -(-65) = 76
c, 30-|-x - 30 | =0
=> |-x - 30 |= 30
=>\(\orbr{\begin{cases}-x-30=30\\-x-30=-30\end{cases}}\)
<=>\(\orbr{\begin{cases}-x=30+30=60\\-x=-30=30=0\end{cases}}\)
<=>\(\orbr{\begin{cases}x=-60\\x=0\end{cases}}\)
mk thử lại rồi nha bn đúng đó nha :))
a,-x+28=34
-x=34-28
-x=6
=>x= -6
Vậy x= -6
b,-57 -(11-x) =8
11-x = -57-8
11-x = -57+ (-8)
11-x = -65
x = 11- (-65)
x = 11+65
x = 76
Vậy x= 76
c, 30 -|-x - 30| = 0
|-x - 30| = 30-0
|-x - 30| =30
Vì |30| = |-30| =30
=> -x - 30 (- { -30 ; 30 }
* -x - 30 = -30
-x = -30 + 30
-x = 0
=> x= 0
* -x - 30 = 30
-x = 30 + 30
-x = 60
=> x = -60
Thử lại : Đúng
Vậy x (- { 0 ; -60 }
\(157-5\left(x+1\right)=57\)
\(5\left(x+1\right)=157-57\)
\(5\left(x+1\right)=100\)
\(x+1=100\div5\)
\(x+1=20\)
\(x=20-1\)
\(x=19\)
157 - 5( x +1 ) = 57
5( x +1 ) = 157 - 57
5( x +1 ) = 100
( x +1 ) = 100 : 5
( x +1 ) = 20
x = 20 - 1
x = 19