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1: \(\Leftrightarrow3x+4=2\)
=>3x=-2
=>x=-2/3
2: \(\Leftrightarrow7x-7=6x-30\)
=>x=-23
3: =>\(5x-5=3x+9\)
=>2x=14
=>x=7
4: =>9x+15=14x+7
=>-5x=-8
=>x=8/5
b: \(ab\cdot bc\cdot ac=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}=\dfrac{1}{4}\)
\(\Leftrightarrow\left(abc\right)^2=\dfrac{1}{4}\)
Trường hợp 1: abc=1/2
\(\Leftrightarrow\left\{{}\begin{matrix}c=\dfrac{1}{2}:\dfrac{1}{2}=1\\a=\dfrac{1}{2}:\dfrac{2}{3}=\dfrac{3}{4}\\b=\dfrac{1}{2}:\dfrac{3}{4}=\dfrac{1}{2}\cdot\dfrac{4}{3}=\dfrac{2}{3}\end{matrix}\right.\)
Trường hợp 2: abc=-1/2
\(\Leftrightarrow\left\{{}\begin{matrix}c=-1\\a=-\dfrac{3}{4}\\b=-\dfrac{2}{3}\end{matrix}\right.\)
c: Theo đề, ta có: \(\left\{{}\begin{matrix}\dfrac{x-1}{2}=\dfrac{y-2}{1}\\\dfrac{y-2}{3}=\dfrac{z-3}{4}\end{matrix}\right.\Leftrightarrow\dfrac{x-1}{6}=\dfrac{y-2}{3}=\dfrac{z-3}{4}\)
Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:
\(\dfrac{x-1}{6}=\dfrac{y-2}{3}=\dfrac{z-3}{4}=\dfrac{2x+3y-z-2-6+3}{2\cdot6-3\cdot6+3\cdot4}=\dfrac{45}{6}=\dfrac{15}{2}\)
Do đó: x-1=45; y-2=45/2; z-3=30
=>x=46; y=49/2; z=33
Ta có:
\(\dfrac{1+3y}{12}=\dfrac{1+7y}{4x}=\dfrac{1+1+3y+7y}{12+4x}\)
\(=\dfrac{2+10y}{2.\left(6+2x\right)}=\dfrac{2.\left(1+5y\right)}{2.\left(6+2x\right)}=\dfrac{1+5y}{6+2x}=\dfrac{1+5y}{5x}\)
- Xét \(1+5y=0\Rightarrow y=\dfrac{-1}{5}\Rightarrow1+5y=0\) ( loại )
- Xét \(1+5y\ne0\Rightarrow6+2x=5x\)
\(\Rightarrow5x-2x=6\)
\(\Rightarrow3x=6\)
\(\Rightarrow x=2\)
Mà \(\dfrac{1+3y}{12}=\dfrac{1+5y}{5x}\)
\(\Rightarrow\dfrac{1+3y}{12}=\dfrac{1+5y}{10}\)
\(\Rightarrow10.\left(1+3y\right)=12.\left(1+5y\right)\)
\(\Rightarrow10+30y=12+60y\)
\(\Rightarrow10-12=60y-30y\)
\(\Rightarrow-2=30y\)
\(\Rightarrow y=\dfrac{-1}{5}\)
Vậy \(x=2\) , \(y=\dfrac{-1}{5}\)
\(1,\dfrac{2x+4}{7}=\dfrac{4x-2}{15}=\dfrac{2.\left(2x+4\right)}{2.7}=\dfrac{4x+8}{14}\)
Áp dụng tính chất của dãy tỉ số bằng nhau ta có :
\(\dfrac{2x+4}{7}=\dfrac{4x-2}{15}==\dfrac{4x+8}{14}=\dfrac{\left(4x+8\right)-\left(4x-2\right)}{14-15}=\dfrac{10}{-1}=-10\)
\(\Rightarrow\dfrac{2x+4}{7}=-10\)
\(\Rightarrow2x+4=-10.7=-70\)
\(\Rightarrow2x=-70+4=-66\)
\(\Rightarrow x=-66:2=-33\)
Vậy \(x=-33\)
\(2,\dfrac{2x+3}{5}=\dfrac{7x-3}{15}=\dfrac{7.\left(2x+3\right)}{7.5}=\dfrac{2.\left(7x-3\right)}{2.15}=\dfrac{14x+21}{35}=\dfrac{14x-6}{30}\)
Áp dụng tính chất của dãy tỉ số bằng nhau ta có :
\(\dfrac{2x+3}{5}=\dfrac{14x+21}{35}=\dfrac{14x-6}{30}=\dfrac{\left(14x+21\right)-\left(14x-6\right)}{35-30}=\dfrac{29}{5}\)
\(\Rightarrow\dfrac{2x+3}{5}=\dfrac{29}{5}\)
\(\Rightarrow2x+3=29\)
\(\Rightarrow2x=29-3=26\)
\(\Rightarrow x=26:2=13\)
\(3,\dfrac{11x-2}{7x+5}=\dfrac{11}{8}\)
\(\Rightarrow\dfrac{11x-2}{11}=\dfrac{7x+5}{8}=\dfrac{7.\left(11x-2\right)}{7.11}=\dfrac{11.\left(7x+5\right)}{8.11}=\dfrac{77x-14}{77}=\dfrac{77x+55}{88}=\dfrac{\left(77x+55\right)-\left(77x-14\right)}{88-77}=\dfrac{69}{11}\)
\(\Rightarrow\dfrac{11x-2}{11}=\dfrac{69}{11}\)
\(\Rightarrow11x-2=69\)
\(\Rightarrow11x=69+2=71\)
\(\Rightarrow x=\dfrac{71}{11}\)
8)\(\frac{4}{9}:\left(-\frac{1}{7}\right)+6\frac{5}{9}:\left(-\frac{1}{7}\right)\)
=\(\frac{4}{9}:\left(-\frac{1}{7}\right)+\frac{59}{9}:\left(-\frac{1}{7}\right)\)
=\(\left(\frac{4}{9}+\frac{59}{9}\right).\left(-7\right)\)
=7.(-7)
=-49
a.
M=\(\dfrac{1}{5}\) . (\(\dfrac{1}{4}\)-\(\dfrac{1}{9}\)+\(\dfrac{1}{9}\)-\(\dfrac{1}{14}\)+\(\dfrac{1}{14}\) - \(\dfrac{1}{19}\)+...+\(\dfrac{1}{44}\)- \(\dfrac{1}{49}\)) . \(\dfrac{2-\left(1+3+5+7+...+49\right)}{89}\)
M = \(\dfrac{1}{5}\) . (\(\dfrac{1}{4}\)- \(\dfrac{1}{49}\)).\(\dfrac{2-\left(12.50+25\right)}{89}\)
M =\(-\dfrac{5.9.7.89}{5.4.7.7.89}=\dfrac{-9}{28}\)
b.
áp dụng tính chất dãy tỉ số bằng nhau ta có :
\(\dfrac{1+3y}{12}=\dfrac{1+5y}{5x}=\dfrac{1+7y}{4x}=\dfrac{1+7y-1-5y}{4x-5x}=\dfrac{2y}{-x}=\dfrac{1+5y-1-3y}{5x-12}=\dfrac{2y}{5x-12}\)=>\(\dfrac{2y}{-x}=\dfrac{2y}{5x-12}\)
=> -x = 5x -12 => x= 2
Thay x= 2 vào trên ta được:
\(\dfrac{1+3y}{12}=\dfrac{2y}{-2}=-y\)
=> 1 = -15y => y= \(\dfrac{-1}{15}\)
Vậy x = 2 và y = \(\dfrac{-1}{5}\)