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Bài làm :
1) \(\frac{x+11}{4}=\frac{2x+4}{5}\)
\(\Leftrightarrow\left(x+11\right).5=4.\left(2x+4\right)\)
\(\Leftrightarrow5x+55=8x+16\)
\(\Leftrightarrow5x-8x=16-55\)
\(\Leftrightarrow-3x=-39\)
\(\Leftrightarrow x=\frac{-39}{-3}=\frac{39}{3}=13\)
2)\(\frac{x+4}{x+10}=\frac{3}{5}\)
\(\Leftrightarrow\left(x+4\right).5=\left(x+10\right).3\)
\(\Leftrightarrow5x+20=3x+30\)
\(\Leftrightarrow5x-3x=30-20\)
\(\Leftrightarrow2x=10\)
\(\Leftrightarrow x=\frac{10}{2}=5\)
3)\(\frac{x+8}{x+14}=\frac{2}{3}\)
\(\Leftrightarrow\left(x+8\right).3=\left(x+14\right).2\)
\(\Leftrightarrow3x+24=2x+28\)
\(\Leftrightarrow3x-2x=28-24\)
\(\Leftrightarrow x=4\)
\(a/\frac{7}{9}-\frac{x}{3}=\frac{1}{9}\)
\(\Rightarrow\frac{x}{3}=\frac{7}{9}-\frac{1}{9}\)
\(\Rightarrow\frac{x}{3}=\frac{2}{3}\)
\(\Rightarrow x=2\)
Vậy \(x=2\)
\(b/\frac{1}{x}-\frac{-2}{15}=\frac{7}{15}\)
\(\Rightarrow\frac{1}{x}=\frac{7}{15}+\frac{-2}{15}\)
\(\Rightarrow\frac{1}{x}=\frac{1}{3}\)
\(\Rightarrow x=3\)
Vậy \(x=3\)
\(c/\frac{-11}{14}-\frac{-4}{x}=\frac{-3}{14}\)
\(\Rightarrow\frac{-4}{x}=\frac{-11}{14}-\frac{-3}{14}\)
\(\Rightarrow\frac{-4}{x}=\frac{-4}{7}\)
\(\Rightarrow x=7\)
Vậy \(x=7\)
\(d/\frac{x}{21}-\frac{2}{3}=\frac{5}{21}\)
\(\Rightarrow\frac{x}{21}=\frac{5}{21}+\frac{2}{3}\)
\(\Rightarrow\frac{x}{21}=\frac{19}{21}\)
\(\Rightarrow x=19\)
Vậy \(x=19\)
#Mạt Mạt#
\(\frac{7}{3}:\left(4.x-1\right)^2-\frac{1}{4}=\frac{1}{3}\)
\(\frac{7}{3}:\left(4.x-1\right)^2=\frac{1}{3}+\frac{1}{4}\)
\(\frac{7}{3}:\left(4.x-1\right)^2=\frac{7}{12}\)
\(\left(4.x-1\right)^2=\frac{7}{3}:\frac{7}{12}\)
\(\left(4.x-1\right)^2=4\)
\(\left(4.x-1\right)^2=2^2\)
\(4.x-1=2\)
\(4.x=2+1\)
\(4.x=3\)
\(x=3:4\)
\(x=0,75\)
\(\frac{A}{B}=\frac{\frac{2000}{1}+\frac{1999}{2}+...+\frac{1}{2000}+2000}{1+\frac{1999}{2}+\frac{1998}{3}+...+\frac{1}{2000}}\)
\(=\frac{\left[\frac{2001}{1}+1\right]+\left[\frac{2001}{2}+1\right]+...+\left[\frac{2001}{2000}+1\right]+2001}{1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2000}}\)
\(=\frac{2001\left[1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2000}\right]}{1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2000}}=2001\)
Giải
Ta có 2/7<x/3<11/4
=> 24/84<24x/84<231/84
=> 24<24x<231
=> 24x thuộc {25;26;...;230}
Nhưng để x thuộc Z thì các phần tử trên phải chi hết cho 24
=> 24x thuộc {48:72;...;216}
=> x thuộc {2;3;...;9} thỏa mãn
Ta có :
\(\frac{2}{7}< \frac{x}{3}< \frac{11}{4}\)
=> \(\frac{24}{84}< \frac{x.28}{84}< \frac{231}{84}\)
=> \(24< x.28< 281\)
Mà \(x.28⋮28\)và \(24< x.28< 281\); \(x.28\in N\)
=> \(x.28\in\left\{28;56;84;112;140;168;196;224;252;280\right\}\)
=> \(x\in\left\{1;2;3;4;5;6;7;8;9;10\right\}\)