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CN
3 tháng 1 2018
\(\left(\dfrac{2}{5}+\dfrac{1}{4}\right)\left(\dfrac{-x}{3}+\dfrac{1}{2}\right)+\dfrac{2}{3}=\dfrac{7}{4}\)
⇔ \(\dfrac{13}{20}\left(\dfrac{-x}{3}+\dfrac{1}{2}\right)=\dfrac{7}{4}-\dfrac{2}{3}\)
⇔ \(\dfrac{13}{20}\left(\dfrac{-x}{3}+\dfrac{1}{2}\right)=\dfrac{13}{12}\)
⇔ \(\dfrac{-x}{3}+\dfrac{1}{2}=\dfrac{13}{12}:\dfrac{13}{20}\)
⇔ \(\dfrac{-x}{3}+\dfrac{1}{2}=\dfrac{5}{3}\)
⇔ \(\dfrac{-x}{3}=\dfrac{5}{3}-\dfrac{1}{2}\)
⇔ \(\dfrac{-x}{3}=\dfrac{7}{6}\)
⇔ \(\dfrac{-2x}{6}=\dfrac{7}{6}\)
⇔ -2x = 7
⇔ \(x=-\dfrac{7}{2}\)
b) \(\left(\dfrac{3}{5}-\dfrac{x}{2}\right)\left(\dfrac{4}{5}+\dfrac{1}{2}\right)-\dfrac{4}{3}=\dfrac{3}{2}\)
⇔ \(\dfrac{13}{10}\left(\dfrac{3}{5}-\dfrac{x}{2}\right)=\dfrac{3}{2}+\dfrac{4}{3}\)
⇔ \(\dfrac{13}{10}\left(\dfrac{3}{5}-\dfrac{x}{2}\right)=\dfrac{17}{6}\)
⇔ \(\dfrac{3}{5}-\dfrac{x}{2}=\dfrac{17}{6}:\dfrac{13}{10}\)
⇔ \(\dfrac{3}{5}-\dfrac{x}{2}=\dfrac{85}{39}\)
⇔ \(\dfrac{x}{2}=\dfrac{3}{5}-\dfrac{85}{39}\)
⇔ \(\dfrac{x}{2}=\dfrac{-308}{195}\)
⇔ \(\dfrac{195x}{390}=\dfrac{-616}{390}\)
⇔ 195x = -616
⇔ \(x=\dfrac{-616}{195}\)
24 tháng 9 2022
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
9 tháng 8 2017
a) \(\dfrac{5}{6}:x=30:3\)
\(\Leftrightarrow\dfrac{5}{6}:x=10\)
\(\Leftrightarrow x=\dfrac{5}{6}:10\)
\(\Leftrightarrow x=\dfrac{1}{12}\)
Vậy .......
b) \(x:2,5=0,003:0,75\)
\(\Leftrightarrow x:2,5=0,004\)
\(\Leftrightarrow x=0,004.2,5\)
\(\Leftrightarrow x=0,01\)
Vậy .......
c) \(3,8:\left(2x\right)=\dfrac{1}{4}:2\dfrac{2}{3}\)
\(\Leftrightarrow3,8:\left(2x\right)=\dfrac{1}{4}:\dfrac{8}{3}=\dfrac{3}{32}\)
\(\Leftrightarrow2x=3,8:\dfrac{3}{32}\)
\(\Leftrightarrow2x=\dfrac{698}{25}\)
\(\Leftrightarrow x=\dfrac{304}{15}\)
Vậy ...
d) \(\dfrac{2}{3}:0,4=x:\dfrac{4}{5}\)
\(\Leftrightarrow x:\dfrac{4}{5}=\dfrac{2}{3}\)
\(\Leftrightarrow x=\dfrac{8}{15}\)
Vậy ....
e) \(3\dfrac{4}{5}:40\dfrac{8}{15}=0,25:x\)
\(\Leftrightarrow0,25:x=\dfrac{19}{5}:\dfrac{608}{15}\)
\(\Leftrightarrow0,25x=\dfrac{57}{608}\)
\(\Leftrightarrow x=\dfrac{228}{608}\)
Vậy ...
e) \(\dfrac{x}{-15}=\dfrac{-60}{x}\)
\(\Leftrightarrow xx=\left(-60\right)\left(-15\right)\)
\(\Leftrightarrow x^2=900\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2=30^2\\x^2=\left(-30\right)^2\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=30\\x=-30\end{matrix}\right.\)
Vậy ...
26 tháng 8 2018
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 \(\dfrac{x-7}{x+8}=\dfrac{x-8}{x+9}\)
\(\Rightarrow\left(x-7\right)\left(x+9\right)=\left(x-8\right)\left(x+8\right)\\ \Leftrightarrow x^2+2x-63=x^2-64\\ \Leftrightarrow2x=-1\\ \Rightarrow x=-\dfrac{1}{2}\)
PT
3 tháng 8 2017
a) \(x+\dfrac{3}{10}=\dfrac{-2}{5}\)
\(x=\dfrac{-2}{5}-\dfrac{3}{10}\)
\(x=\dfrac{-7}{10}\)
b) \(x+\dfrac{5}{6}=\dfrac{2}{5}-\left(-\dfrac{2}{3}\right)\)
\(x+\dfrac{5}{6}=\dfrac{2}{5}+\dfrac{2}{3}\)
\(x+\dfrac{5}{6}=\dfrac{16}{15}\)
\(x=\dfrac{16}{15}-\dfrac{5}{6}\)
\(x=\dfrac{7}{30}\)
c) \(1\dfrac{2}{5}x+\dfrac{3}{7}=-\dfrac{4}{5}\)
\(\dfrac{7}{5}x+\dfrac{3}{7}=-\dfrac{4}{5}\)
\(\dfrac{7}{5}x=-\dfrac{4}{5}-\dfrac{3}{7}\)
\(\dfrac{7}{5}x=\dfrac{-43}{35}\)
\(\Rightarrow x=\dfrac{-43}{49}\)
d) \(\left[x+\dfrac{3}{4}\right]-\dfrac{1}{3}=0\)
\(\left[x+\dfrac{3}{4}\right]=0+\dfrac{1}{3}\)
\(\left[x+\dfrac{3}{4}\right]=\dfrac{1}{3}\)
\(x=\dfrac{1}{3}-\dfrac{3}{4}\)
\(x=\dfrac{-5}{12}\)
e) \(\left[x+\dfrac{4}{5}\right]-\left(-3,75\right)=-\left(-2,15\right)\)
\(\left[x+\dfrac{4}{5}\right]+3,75=2,15\)
\(x+\dfrac{4}{5}=2,15-3,75\)
\(x+\dfrac{4}{5}=-\dfrac{8}{5}\)
\(x=\dfrac{-8}{5}-\dfrac{4}{5}\)
\(x=\dfrac{-12}{5}\)
f) \(\left(x-2\right)^2=1\)
\(\Rightarrow x=1\)
Sức chịu đựng có giới hạn -.-
NH
3 tháng 8 2017
- Mình tiếp tục cho Nguyễn Phương Trâm nhé.
g, \(\left(2x-1\right)^3=-27\)
\(\Rightarrow\left(2x-1\right)^3=\left(-3\right)^3\)
\(\Rightarrow2x-1=-3\)
\(\Rightarrow2x=-2\)
=> \(x=-1\)
- Vậy x = -1
h,\(\dfrac{x-1}{-15}=-\dfrac{60}{x-1}\)
\(\Rightarrow\left(x-1\right)^2=-60.\left(-15\right)\)
\(\Rightarrow\left(x-1\right)^2=900 \)
\(\Rightarrow\left(x-1\right)^2=30^2\Rightarrow x-1=30\)
=> x = 31
i,\(x:\left(\dfrac{-1}{2}\right)^3=\dfrac{-1}{2}\)
=> \(x:\left(-\dfrac{1}{8}\right)=-\dfrac{1}{2}\)
\(\Rightarrow x=\dfrac{1}{16}\)
- Vậy x=\(\dfrac{1}{16}\)
j, \(\left(\dfrac{3}{4}\right)^5.x=\left(\dfrac{3}{4}\right)^7\)
\(\Rightarrow \left(\dfrac{3}{4}\right).x=\left(\dfrac{3}{4}\right)^2\)
\(\Rightarrow x=\left(\dfrac{3}{4}\right)^2:\dfrac{3}{4}\)
\(\Rightarrow x=\dfrac{3}{4}\)
- Vạy x = \(\dfrac{3}{4}\)
k, \(8^x:2^x=4\Rightarrow\left(8:2\right)^x=4\)
=>\(4^x=4\)
=> x = 1
- Vậy x = 1
24 tháng 10 2017
\(A=\left|x-\dfrac{1}{2}\right|+\dfrac{3}{4}\\ \text{Do }\left|x-\dfrac{1}{2}\right|\ge0\forall x\\ A=\left|x-\dfrac{1}{2}\right|+\dfrac{3}{4}\ge\dfrac{3}{4}\forall x\)
Dấu \("="\) xảy ra khi :
\(\left|x-\dfrac{1}{2}\right|=0\\ \Leftrightarrow x-\dfrac{1}{2}=0\\ \Leftrightarrow x=\dfrac{1}{2}\)
Vậy \(A_{\left(Min\right)}=\dfrac{3}{4}\) khi \(x=\dfrac{1}{2}\)
\(B=2-\left|x+\dfrac{5}{6}\right|\\ \text{Do }\left|x+\dfrac{5}{6}\right|\ge0\forall x\\ \Rightarrow B=2-\left|x+\dfrac{5}{6}\right|\le2\forall x\)
Dấu \("="\) xảy ra khi :
\(\left|x+\dfrac{5}{6}\right|=0\\ \Leftrightarrow x+\dfrac{5}{6}=0\\ \Leftrightarrow x=-\dfrac{5}{6}\)
Vậy \(B_{\left(Max\right)}=2\) khi \(x=-\dfrac{5}{6}\)
GP
3
VT
9 tháng 11 2017
\(\dfrac{3x}{5}=\dfrac{2y}{3}\Leftrightarrow\dfrac{3x}{5}.\dfrac{1}{6}=\dfrac{2y}{3}.\dfrac{1}{6}\Leftrightarrow\dfrac{3x}{30}=\dfrac{2y}{18}\Leftrightarrow\dfrac{x}{10}=\dfrac{y}{9}\Leftrightarrow\dfrac{x^2}{100}=\dfrac{y^2}{81}\)Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{x^2}{100}=\dfrac{y^2}{81}=\dfrac{x^2-y^2}{100-81}=\dfrac{38}{19}=2\)
\(\Rightarrow\left\{{}\begin{matrix}x^2=2.100=200\\y^2=2.81=162\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\pm\sqrt{200}\\y=\pm\sqrt{162}\end{matrix}\right.\)
NN
9 tháng 11 2017
\(\dfrac{3}{5}x=\dfrac{2}{3}y\Rightarrow\dfrac{x}{\dfrac{2}{3}}=\dfrac{y}{\dfrac{3}{5}}\) và \(x^2-y^2=38\)
Áp dụng tính chất dãy tỉ số bằng nhau:
\(\dfrac{x}{\dfrac{2}{3}}=\dfrac{y}{\dfrac{3}{5}}=\dfrac{x^2}{\dfrac{4}{6}}=\dfrac{y^2}{\dfrac{6}{10}}=\dfrac{x^2+y^2}{\dfrac{4}{6}+\dfrac{6}{10}}=\dfrac{38}{\dfrac{19}{15}}=30\)
\(\dfrac{x}{\dfrac{2}{3}}=30\Rightarrow x=30.\dfrac{2}{3}=20\)
\(\dfrac{y}{\dfrac{3}{5}}=30\Rightarrow y=30.\dfrac{3}{5}=18\)
Vậy x=20 ; y=18
15 tháng 6 2022
a: |x-1/2|=7/2
=>x-1/2=7/2 hoặc x-1/2=-7/2
=>x=4 hoặc x=-3
b: \(x:\dfrac{3}{8}+\dfrac{5}{8}=x\)
=>8/3x-x=-5/8
=>5/3x=-5/8
hay x=-5/8:5/3=-5/8x3/5=-15/40=-3/8
c: \(\dfrac{5}{6}-\left|x-\dfrac{1}{2}\right|=\dfrac{15}{18}=\dfrac{5}{6}\)
=>|x-1/2|=0
=>x-1/2=0
hay x=1/2
e: \(\left(5x-3\right)^2-\dfrac{1}{64}=0\)
=>(5x-3)2=1/64
=>5x-3=1/8 hoặc 5x-3=-1/8
=>5x=25/8 hoặc 5x=23/8
=>x=5/8 hoặc x=23/40
LN
9 tháng 11 2018
a,\(x-\dfrac{3}{5}=\dfrac{3}{5}\)
\(x=\dfrac{3}{5}+\dfrac{3}{5}\)
\(x=\dfrac{6}{5}\)
b,\(\left|x\right|-\dfrac{4}{5}=\dfrac{2}{5}\)
\(\left|x\right|=\dfrac{2}{5}+\dfrac{4}{5}\)
\(\left|x\right|=\dfrac{6}{5}\)
\(\Rightarrow x=\pm\dfrac{6}{5}\)
c,\(\dfrac{x}{-5}=\dfrac{24}{15}\)
\(x=\dfrac{-5.24}{15}\)
\(x=\dfrac{-24}{5}\)
d,Áp dụng tc dãy TSBN, ta có:
\(\dfrac{x}{4}=\dfrac{y}{5}=\dfrac{x-y}{4-5}=\dfrac{21}{-1}=-21\)
+\(\dfrac{x}{4}=-21\Rightarrow x=-21.4=-84\)
+\(\dfrac{y}{5}=-21\Rightarrow y=-21.5=-105\)
Vậy x=-84 ; y=-105
9 tháng 11 2018
a/ \(x-\dfrac{3}{5}=\dfrac{3}{5}\)
\(\Leftrightarrow x=\dfrac{3}{5}+\dfrac{3}{5}\)
\(\Leftrightarrow x=\dfrac{6}{5}\)
Vậy...
b/ \(\left|x\right|-\dfrac{4}{5}=\dfrac{2}{5}\)
\(\Leftrightarrow\left|x\right|=\dfrac{2}{5}+\dfrac{4}{5}\)
\(\Leftrightarrow\left|x\right|=\dfrac{6}{5}\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{6}{5}\\x=-\dfrac{6}{5}\end{matrix}\right.\)
Vậy...
c/ \(\dfrac{x}{-5}=\dfrac{24}{15}\)
\(\Leftrightarrow15x=-120\)
\(\Leftrightarrow x=-8\)
Vậy...
c/ Theo t/c dãy tỉ số bằng nhau ta có :
\(\dfrac{x}{4}=\dfrac{y}{5}=\dfrac{x-y}{4-5}=\dfrac{21}{-1}=-21\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{x}{4}=-21\\\dfrac{y}{5}=-21\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=-84\\y=-105\end{matrix}\right.\)
Vậy..
x=9
x=9