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a) \(2x\left(x-3\right)+6\left(3-x\right)=0\)
\(\Leftrightarrow2\left[x\left(x-3\right)+3\left(3-x\right)\right]=0\)
\(\Leftrightarrow x\left(x-3\right)+3\left(3-x\right)=0\)
\(\Leftrightarrow x-3=0\)
\(\Rightarrow x=3\)
b) \(3x\left(2x-5\right)-15\left(5-2x\right)=0\)
\(\Leftrightarrow3\left[x\left(2x-5\right)-5\left(5-2x\right)\right]=0\)
\(\Leftrightarrow x\left(2x-5\right)-5\left(5-2x\right)=0\)
\(\Leftrightarrow\left(x+5\right)\left(2x-5\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x+5=0\\2x-5=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=-5\\x=\frac{5}{2}\end{cases}}\)
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a) \(5-\frac{2x}{3}=4x-\frac{1}{-5}\)
\(\frac{75-10x}{15}=\frac{60x+3}{15}\)
75 - 10x = 60x +3
72 = 70x
\(\frac{72}{70}\) = x
x =\(\frac{36}{35}\)
Vậy x = \(\frac{36}{35}\)
b) \(2x-\frac{10}{6}=\frac{-27}{5}-x\)
\(2x-\frac{5}{3}=\frac{-27}{5}-x\)
\(\frac{30x-25}{15}=\frac{-81-15}{15}\)
30x =-96+25
30x =-71
x= -71/30
Vậy x= -71/30
c) \(13x-\frac{2}{2x}+5=\frac{76}{17}\)
13x - 1/x +5 = 76/17
\(\frac{221x-17+85}{17x}=\frac{76x}{17x}\)
221x +68 = 76x
221x-76x =-68
145x =-68
x =\(\frac{-68}{145}\)
Vậy .........
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\(a,\frac{1}{2}x+\frac{5}{2}=\frac{7}{2}x-\frac{3}{4}\)
\(\Leftrightarrow\frac{1}{2}x+\frac{5}{2}-\frac{7}{2}x=-\frac{3}{4}\)
\(\Leftrightarrow\frac{1}{2}x-\frac{7}{2}x+\frac{5}{2}=-\frac{3}{4}\)
\(\Leftrightarrow-3x+\frac{5}{2}=-\frac{3}{4}\)
\(\Leftrightarrow-3x=-\frac{13}{4}\)
\(\Leftrightarrow x=-\frac{13}{4}:(-3)=-\frac{13}{4}:\frac{-3}{1}=-\frac{13}{4}\cdot\frac{-1}{3}=\frac{13}{12}\)
\(b,\frac{2}{3}x-\frac{2}{5}=\frac{1}{2}x-\frac{1}{3}\)
\(\Leftrightarrow\frac{2}{3}x-\frac{2}{5}-\frac{1}{2}x=-\frac{1}{3}\)
\(\Leftrightarrow\frac{2}{3}x-\frac{1}{2}x-\frac{2}{5}=-\frac{1}{3}\)
\(\Leftrightarrow\frac{1}{6}x-\frac{2}{5}=-\frac{1}{3}\)
\(\Leftrightarrow\frac{1}{6}x=\frac{1}{15}\)
\(\Leftrightarrow x=\frac{1}{15}:\frac{1}{6}=\frac{1}{15}\cdot6=\frac{6}{15}=\frac{2}{5}\)
\(c,\frac{1}{3}x+\frac{2}{5}(x+1)=0\)
\(\Leftrightarrow\frac{1}{3}x+\frac{2}{5}x+\frac{2}{5}=0\)
\(\Leftrightarrow\frac{11}{15}x=-\frac{2}{5}\)
\(\Leftrightarrow x=-\frac{6}{11}\)
d,e,f Tương tự
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| 3x + 5| = | 3-2x|
TH1: 3x + 5 = 3 - 2x
=> 3x + 2x = 3-5
5x = -2
x = -2/5
TH2: 3x + 5 = -3 + 2x
=> 3x - 2x = -3 -5
x = -8
KL: x = -2/5 hoặc x = -8
| 3x + 5 | = | 3 - 2x |
3x+5 = 3-2x
3x-2x = 3-5
1x = 2
Vậy ................................
![](https://rs.olm.vn/images/avt/0.png?1311)
Câu a lập bảng xét dấu
b) \(3x-\left|x+15\right|=\frac{5}{4}\)
\(\Rightarrow\left|x+15\right|=3x-\frac{5}{4}\)
\(\Rightarrow\orbr{\begin{cases}x+15=3x-\frac{5}{4}\\x+15=-3x+\frac{5}{4}\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}-2x=\frac{-64}{4}\\4x=\frac{-55}{4}\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=8\\x=\frac{-55}{16}\end{cases}}\)
\(\left|2x-1\right|-\left|x+\frac{1}{3}\right|=0\)
=> \(\left|2X-1\right|=\left|X+\frac{1}{3}\right|\)
=> \(2X-1=\pm\left(X+\frac{1}{3}\right)\)
\(TH1:2x-1=x+\frac{1}{3}\) \(TH2:2x-1=-\left(x+\frac{1}{3}\right)\)
=> \(2x-x=\frac{1}{3}+1\) => \(2x-1=-x-\frac{1}{3}\)
=>\(x=\frac{4}{3}\) => \(2x+x=-\frac{1}{3}+1\)
=> \(3x=-\frac{2}{3}=>x=-\frac{2}{9}\)
Nếu x > 0
\(\Rightarrow\hept{\begin{cases}|2x-5|=2x-5\\|2x-15|=2x-15\end{cases}}\)
\(\Leftrightarrow2x-5+2x-15=10\)
\(\Leftrightarrow4x=30\)
\(\Leftrightarrow x=\frac{15}{2}\)
Nếu x < 0
\(\Rightarrow\hept{\begin{cases}|2x-5|=-2x+5\\|2x-15|=-2x+15\end{cases}}\)
\(\Leftrightarrow-2x+5-2x+15=10\)
\(\Leftrightarrow-4x=-10\)
\(\Leftrightarrow x=\frac{5}{2}\)
Vậy...
\(\Rightarrow20-4x=10\) với x\(\ge\)\(\frac{5}{2}\)
\(\Rightarrow4x=10\)
\(\Rightarrow x=\frac{5}{2}\)(t/m)
\(\Rightarrow-10=10\) (loại) với \(\frac{5}{2}< x< \frac{15}{2}\)
\(\Rightarrow4x-10=10\)với x\(\le\frac{15}{2}\)
\(\Rightarrow4x=20\Rightarrow x=5\)
Vậy x=...........
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