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\(\frac{x+2}{17}+\frac{x+4}{15}+\frac{x+6}{13}=\frac{x+8}{11}+\frac{x+10}{9}+\frac{x+12}{7}\)
\(\Rightarrow\left(\frac{x+2}{17}+1\right)+\left(\frac{x+4}{15}+1\right)+\left(\frac{x+6}{13}+1\right)-\left(\frac{x+8}{11}+1\right)-\left(\frac{x+10}{9}+1\right)-\left(\frac{x+12}{7}+1\right)=0\)
\(\Rightarrow\frac{x+19}{17}+\frac{x+19}{15}+\frac{x+19}{13}-\frac{x+19}{11}-\frac{x+19}{10}-\frac{x+19}{7}=0\)
\(\Rightarrow\left(x+19\right)(\frac{1}{17}+\frac{1}{15}+\frac{1}{13}-\frac{1}{11}-\frac{1}{9}-\frac{1}{7})\)
\(\Rightarrow x+19=0\)\(\left(Vì\frac{1}{17}+\frac{1}{15}+\frac{1}{13}-\frac{1}{11}-\frac{1}{9}-\frac{1}{7}\ne0\right)\)
\(\Rightarrow x=-19\)
Ta có : \(\frac{x+2}{17}+\frac{x+4}{15}+\frac{x+6}{13}=\frac{x+8}{11}+\frac{x+10}{9}+\frac{x+12}{7}\)
\(\Rightarrow\left(\frac{x+2}{17}+1\right)+\left(\frac{x+4}{15}+1\right)+\left(\frac{x+6}{13}+1\right)=\left(\frac{x+8}{11}+1\right)+\left(\frac{x+10}{9}+1\right)+\left(\frac{x+12}{7}+1\right)\)
\(\Rightarrow\frac{x+19}{17}+\frac{x+19}{15}+\frac{x+19}{13}-\frac{x+19}{11}-\frac{x+19}{9}-\frac{x+19}{7}=0\)
\(\Rightarrow\left(x+19\right)\left(\frac{1}{17}+\frac{1}{15}+\frac{1}{13}-\frac{1}{11}-\frac{1}{9}-\frac{1}{7}\right)=0\)
\(\Rightarrow x+19=0\Rightarrow x=-19\)
a) \(\frac{3}{x}\ge1\)
\(\Leftrightarrow\frac{3}{x}\ge\frac{x}{x}\)
\(\Leftrightarrow3\ge x\)
\(\Leftrightarrow x\in\left\{1;2;3\right\}\) < vì x là các số nguyên dương>
VẬY \(x\in\left\{1;2;3\right\}\)
b) \(\frac{8}{x}< \frac{x}{3}< \frac{9}{x}\)
\(\Leftrightarrow\frac{24}{3x}< \frac{x^2}{3x}< \frac{27}{3x}\)
\(\Leftrightarrow24< x^2< 27\)
\(\Leftrightarrow\sqrt{24}< x< \sqrt{27}\)
\(\Leftrightarrow4,9< x< 5,2\) <Lưu ý căn 24 và căn 27 đã được làm tròn để viết cho gọn>
\(\Leftrightarrow x=5\) <vì x là số nguyên dương>
VẬY \(x=5\)
\(\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{4}\right)+\left(x+\frac{1}{8}\right)+\left(x+\frac{1}{16}\right)=1\)
\(\Rightarrow x+\frac{1}{2}+x+\frac{1}{4}+x+\frac{1}{8}+x+\frac{1}{16}=1\)
\(\Rightarrow\left(x+x+x+x\right)+\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right)=1\)
\(\Rightarrow4x+\frac{15}{16}=1\)
\(\Rightarrow4x=1-\frac{15}{16}\)
\(\Rightarrow4x=\frac{1}{16}\)
\(\Rightarrow x=\frac{1}{16}:4\)
\(\Rightarrow x=\frac{1}{64}\)
\(\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{4}\right)+\left(x+\frac{1}{8}\right)+\left(x+\frac{1}{16}\right)=1\)
\(4x+\frac{8}{16}+\frac{4}{16}+\frac{2}{16}+\frac{1}{16}=1\)
\(4x+\frac{15}{16}=1\)
\(4x=\frac{1}{16}\)
\(x=\frac{1}{64}\)
Vậy......
Ta có : \(2\frac{x}{7}=\frac{2.7+x}{7}=\frac{14+x}{7}\)
Nên : \(\frac{14+x}{7}=\frac{2x+9}{7}\)
<=> 14 + x = 2x + 9
=> 14 - 9 = 2x - x
=> x = 5
Vậy x = 5
14+x7 =2x+97
<=> 14 + x = 2x + 9
=> 14 - 9 = 2x - x
=> x = 5
Vậy x = 5
a.2/3 + 1/3 - x= 3/5
=> 1-x = 3/5
=> x = 1-3/5= 2/5
b. 1/8/15 - 2/3x = 0,2
=> 2/3x= 23/15 - 1/5= 4/3
=> x= 4/3 : 2/3=2
c. 2/3x -3/2x = 5/12
=> x( 2/3 - 3/2) = 5/12
=> x. -5/6 = 5/12
=> x= 5/12 : -5/6
=> x= -1/2
a) 2/3 + 1/3 - x = 3/5
=> 1 - x = 3/5
=> x = 1 - 3/5
x = 2/5
b) \(1\frac{8}{15}-\frac{2}{3}x=0,2\)
=> 23/15 - 2/3x = 0,2
=> 2/3x = 23/15 - 0,2
2/3x = 1,333333333
=>x = 1,333333333 : 2/3
x = 2
c) ???
Bài 1 :
\(\frac{4}{x}=\frac{x+1}{5}\)
\(\Rightarrow x\cdot\left(x+1\right)=4\cdot5\)
\(\Rightarrow x\cdot\left(x+1\right)=20\)
Vì \(x\cdot\left(x+1\right)\)là tích của sai số tự nhiên liên tiếp bằng 20
\(\Rightarrow4\cdot5=20\)
\(\Rightarrow x=4\)
Bài 2 :
\(\frac{7}{x-1}=\frac{x}{8}\)
\(\Rightarrow\left(x-1\right)\cdot x=7\cdot8\)
\(\Rightarrow\left(x-1\right)\cdot x=56\)
Vì \(\left(x-1\right)\cdot x\)là tích của hai số tự nhiên liên tiếp bằng 56
\(\Rightarrow7\cdot8=56\)
\(\Rightarrow x=7\)
1) \(\frac{4}{x}=\frac{x+1}{5}\)
\(\Rightarrow x.\left(x+1\right)=4.5\) ( x; x + 1 là 2 số tự nhiên liên tiếp)
=> x = 4
2) \(\frac{7}{x-1}=\frac{x}{8}\Rightarrow\left(x-1\right).x=7.8\) ( x-1;x là 2 số tự nhiên liên tiếp)
=> x = 8
\(\frac{x-5}{3}=\frac{6}{5}\)
\(x-5=\frac{6}{5}.3\)
\(x-5=\frac{18}{5}\)
\(x=\frac{18}{5}+5\)
\(\Rightarrow x=\frac{43}{5}\)
Vậy ...
\(\frac{1}{3}=\frac{2-x}{4}\)
\(\frac{4}{3}=2-x\)
\(x=2-\frac{4}{3}\)
\(\Rightarrow x=\frac{2}{3}\)
Vậy ...
\(\frac{x}{-2}=\frac{-8}{x}\Leftrightarrow x^2=\left(-2\right).\left(-8\right)=16=4^2;\left(-4\right)^2\Rightarrow x=\left\{4;-4\right\}\)
\(\frac{x}{-2}=\frac{-8}{x}\Rightarrow x^2=16\Leftrightarrow\text{[}x=4;x=-4\text{]}\)