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\(\frac{x+22}{11}+\frac{x+23}{12}=\frac{x+24}{13}+\frac{x+25}{14}\)
\(\Leftrightarrow\left(\frac{x+22}{11}+1\right)+\left(\frac{x+23}{12}+1\right)=\left(\frac{x+24}{13}+1\right)+\left(\frac{x+25}{14}+1\right)\)
\(\Leftrightarrow\frac{x+33}{11}+\frac{x+35}{12}=\frac{x+37}{13}+\frac{x+39}{14}\)
\(\Leftrightarrow\frac{x+33}{11}+\frac{x+35}{12}-\frac{x+37}{13}-\frac{x+39}{14}=0\)
\(\Leftrightarrow\frac{2184\cdot\left(x+33\right)+2002\cdot\left(x+35\right)-1848\cdot\left(x+37\right)-1716\cdot\left(x+39\right)}{24024}=0\)
\(\Leftrightarrow2184x+72072+2002x+70070-1848x-68376-1716x-66924=0\)
\(\Leftrightarrow622x+6842=0\)
\(\Leftrightarrow x=-11\)
Bài 3:
\(a,\dfrac{x-1}{10}+\dfrac{x-1}{11}=\dfrac{x-1}{12}+\dfrac{x-1}{13}\)
\(\Rightarrow\dfrac{x-1}{10}+\dfrac{x-1}{11}-\dfrac{x-1}{12}-\dfrac{x-1}{13}=0\)
\(\Rightarrow\left(x-1\right)\left(\dfrac{1}{10}+\dfrac{1}{11}-\dfrac{1}{12}-\dfrac{1}{13}\right)=0\)
Mà \(\dfrac{1}{10}+\dfrac{1}{11}-\dfrac{1}{12}-\dfrac{1}{13}\ne0\)
\(\Rightarrow x-1=0\Rightarrow x=1\)
Vậy x = 1
b, \(\dfrac{x-2000}{10}+\dfrac{x-1999}{9}=\dfrac{x-1998}{8}+\dfrac{x-1997}{7}\)
\(\Rightarrow\dfrac{x-2000}{10}+1+\dfrac{x-1999}{9}+1=\dfrac{x-1998}{8}+\dfrac{x-1997}{7}+1\)
\(\Rightarrow\dfrac{x-1990}{10}+\dfrac{x-1990}{9}-\dfrac{x-1990}{8}-\dfrac{x-1990}{7}=0\)
\(\Rightarrow\left(x-1990\right)\left(\dfrac{1}{10}+\dfrac{1}{9}-\dfrac{1}{8}-\dfrac{1}{7}\right)=0\)
Mà \(\dfrac{1}{10}+\dfrac{1}{9}-\dfrac{1}{8}-\dfrac{1}{7}\ne0\)
\(\Rightarrow x-1990=0\Rightarrow x=1990\)
Câu 1:
a) 25-(30+x) = x-(27-8)
25-30-x = x-19
-5-x = x-19
(-5)+19 = x+x
14 = 2x
x = 7
Vậy x = 7
b) (x-12)-15 = (20-7)-(18+x)
x-12-15 = 13-18-x
x-(12+15)= -5-x
x-27 = -5-x
x+x = -5+27
2x = 22
x = 11
Câu 2:
a) 4573+46-4573+35-16-5
= (4573-4573)+(46-16)+(35-5)
= 0+30+30
= 60
b) 32+34+36+38-10-12-14-16-18
= (32-12)+(34-14)+(36-16)+(38-18)-10
= 10+10+10+10-10
= 30
1, a) 25 - (30 + x) = x - (27 - 8)
25 - 30 - x = x - 27 + 8
-x - x = -27 + 8 - 25 + 30
-2x = -14
x = -14 : (-2)
x = 7
b) (x - 12) - 15 = (20 - 7) - (18 + x)
x - 12 - 15 = 20 - 7 - 18 - x
x + x = 20 - 7 - 18 + 12 + 15
2x = 22
x = 22 : 2
x = 11
2, a) 4573 + 46 - 4573 + 35 - 16 - 5
= (4573 - 4573) + (46 - 16) + (35 - 5)
= 0 + 30 + 30
= 60
b) 32 + 34 + 36 + 38 - 10 - 12 - 14 - 16 - 18
= (32 - 10) + (34 - 12) + (36 - 14) + (38 - 16) - 18
= 22 + 22 + 22 + 22 - 18
= 22 x 4 - 18
= 88 - 18
= 70
có số số hạng la ( 100 - 14 ) : 2 + 1 = 44
vì h trên có 44 số nguyên âm chẵn
=> tích la số nguyên dương