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\(1,\dfrac{2x+4}{7}=\dfrac{4x-2}{15}=\dfrac{2.\left(2x+4\right)}{2.7}=\dfrac{4x+8}{14}\)
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 :
\(\dfrac{2x+3}{5}=\dfrac{14x+21}{35}=\dfrac{14x-6}{30}=\dfrac{\left(14x+21\right)-\left(14x-6\right)}{35-30}=\dfrac{29}{5}\)
\(\Rightarrow\dfrac{2x+3}{5}=\dfrac{29}{5}\)
\(\Rightarrow2x+3=29\)
\(\Rightarrow2x=29-3=26\)
\(\Rightarrow x=26:2=13\)
\(3,\dfrac{11x-2}{7x+5}=\dfrac{11}{8}\)
\(\Rightarrow\dfrac{11x-2}{11}=\dfrac{7x+5}{8}=\dfrac{7.\left(11x-2\right)}{7.11}=\dfrac{11.\left(7x+5\right)}{8.11}=\dfrac{77x-14}{77}=\dfrac{77x+55}{88}=\dfrac{\left(77x+55\right)-\left(77x-14\right)}{88-77}=\dfrac{69}{11}\)
\(\Rightarrow\dfrac{11x-2}{11}=\dfrac{69}{11}\)
\(\Rightarrow11x-2=69\)
\(\Rightarrow11x=69+2=71\)
\(\Rightarrow x=\dfrac{71}{11}\)
a)A=\(x^5-\dfrac{1}{2}x+7x^3-2x+\dfrac{1}{5}x^3+3x^4-x^5+\dfrac{2}{5}x^4+15\)
=\(=\dfrac{-5}{2}x+\dfrac{36}{5}x^3+\dfrac{17}{5}x^4+15\)
b)B=\(3x^2-10+\dfrac{2}{5}x^3+7x-x^2+8+7x^2\)
\(=9x^2+\dfrac{2}{5}x^3+7x+2\)
c)C=\(\dfrac{1}{7}x-2x^4+5x+6\)
câu E
\(\left\{{}\begin{matrix}x\ne\dfrac{5}{2}\\\left(2x-5\right)\left(5-2x\right)=-\left(\dfrac{3}{2}\right)^4\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ne\dfrac{5}{2}\\\left|2x-5\right|=\left(\dfrac{3}{2}\right)^2\end{matrix}\right.\)
\(\left[{}\begin{matrix}\left\{{}\begin{matrix}x< \dfrac{5}{2}\\2x-5=-\left(\dfrac{3}{2}\right)^2\Rightarrow x=\dfrac{11}{8}< \dfrac{5}{2}\left(n\right)\end{matrix}\right.\\\left\{{}\begin{matrix}x>\dfrac{5}{2}\\2x-5=\left(\dfrac{3}{2}\right)^2\Rightarrow x=\dfrac{29}{8}>\dfrac{5}{2}\left(n\right)\end{matrix}\right.\end{matrix}\right.\)
câu F (bạn cho vào lớp 7.2=lớp 14 nhé. )
b: =>(3x-1)(3x+1)(2x+3)=0
hay \(x\in\left\{\dfrac{1}{3};-\dfrac{1}{3};-\dfrac{3}{2}\right\}\)
c: \(\Leftrightarrow\left|2x-\dfrac{1}{3}\right|=\dfrac{5}{6}+\dfrac{3}{4}=\dfrac{19}{12}\)
=>2x-1/3=19/12 hoặc 2x-1/3=-19/12
=>2x=23/12 hoặc 2x=-15/12=-5/4
=>x=23/24 hoặc x=-5/8
d: \(\Leftrightarrow-\dfrac{5}{6}\cdot x+\dfrac{3}{4}=-\dfrac{3}{4}\)
=>-5/6x=-3/2
=>x=3/2:5/6=3/2*6/5=18/10=9/5
e: =>2/5x-1/2=3/4 hoặc 2/5x-1/2=-3/4
=>2/5x=5/4 hoặc 2/5x=-1/4
=>x=5/4:2/5=25/8 hoặc x=-1/4:2/5=-1/4*5/2=-5/8
f: =>14x-21=9x+6
=>5x=27
=>x=27/5
h: =>(2/3)^2x+1=(2/3)^27
=>2x+1=27
=>x=13
i: =>5^3x*(2+5^2)=3375
=>5^3x=125
=>3x=3
=>x=1
1: \(\Leftrightarrow\left(x+1\right)^2=4\)
=>x+1=2 hoặc x+1=-2
=>x=1 hoặc x=-3
2: \(\Leftrightarrow7x-21=5x+25\)
=>2x=46
=>x=23
3: \(\Leftrightarrow x^2+4x+3=x^2+0.5x+4x+2\)
=>4,5x+2=4x+3
=>x=1
1: =>1/3:x=3/5-2/3=9/15-10/15=-1/15
=>x=-1/3:1/15=5
2: \(\Leftrightarrow x\cdot\dfrac{2}{3}-3=\dfrac{2}{5}\cdot\left(-10\right)=-4\)
=>x*2/3=-1
=>x=-3/2
3: \(\Leftrightarrow\dfrac{8}{3}:x=\dfrac{25}{12}:\dfrac{-3}{50}=\dfrac{25}{12}\cdot\dfrac{-50}{3}\)
hay x=-48/625
9: =>x=-2*3/1,5=-4
8: =>2/3:x=5/2:-3/10=5/2*(-10)/3=-50/6=-25/3
=>x=-2/3:25/3=-2/3*3/25=-2/25
3. Từ \(\dfrac{x-2}{27}=\dfrac{3}{x-2}\Rightarrow\left(x-2\right)^2=81\)
\(\Rightarrow\left(x-2\right)^2=\left(\pm9\right)^2\\ \Rightarrow\left[{}\begin{matrix}x-2=-9\\x-2=9\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-7\\x=11\end{matrix}\right.\)
Vậy x = -7 hoặc x = 11
4. Từ \(\dfrac{2x+5}{9-2x}=\dfrac{2}{5}\)
\(\Rightarrow5\left(2x+5\right)=2\left(9-2x\right)\\ \Leftrightarrow10x+25=18-4x\\ \Leftrightarrow14x=-7\\ \Rightarrow x=-\dfrac{1}{2}\)
5. Từ \(\dfrac{x-7}{x+8}=\dfrac{x-8}{x+9}\)
\(\Rightarrow\left(x-7\right)\left(x+9\right)=\left(x-8\right)\left(x+8\right)\\ \Leftrightarrow x^2+2x-63=x^2-64\\ \Leftrightarrow2x=-1\\ \Rightarrow x=-\dfrac{1}{2}\)
1) -2/3
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