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3x - 7 = 2x + 5
3x - 2x = 5 + 7
x = 12
|3x - 2| = 7
\(\Rightarrow\left\{\begin{matrix}3x-2=7\\-\left(3x-2\right)=7\end{matrix}\right.\Rightarrow\left\{\begin{matrix}3x=9\\-3x+2=7\end{matrix}\right.\)
\(\Rightarrow\left\{\begin{matrix}x=3\\-3x=5\end{matrix}\right.\Rightarrow\left\{\begin{matrix}x=3\\x=-\frac{5}{3}\end{matrix}\right.\)
4 - |x - 2| = -3
|x - 2| = 4 - (-3)
|x - 2| = 7
\(\Rightarrow\left\{\begin{matrix}x-2=7\\-\left(x-2\right)=7\end{matrix}\right.\Rightarrow\left\{\begin{matrix}x=9\\-x+2=7\end{matrix}\right.\)
\(\Rightarrow\left\{\begin{matrix}x=9\\-x=5\end{matrix}\right.\Rightarrow\left\{\begin{matrix}x=9\\x=-5\end{matrix}\right.\)
|2x - 3| = x - 1
\(\Rightarrow\left\{\begin{matrix}2x-3=x-1\\-\left(2x-3\right)=x-1\end{matrix}\right.\Rightarrow\left\{\begin{matrix}2x-x=-1+3\\-2x+3=x-1\end{matrix}\right.\)
\(\Rightarrow\left\{\begin{matrix}x=2\\-2x-x=-1-3\end{matrix}\right.\Rightarrow\left\{\begin{matrix}x=2\\-3x=-4\end{matrix}\right.\)
\(\Rightarrow\left\{\begin{matrix}x=2\\x=\frac{4}{3}\end{matrix}\right.\)
|3x + 1| = x + 3
\(\Rightarrow\left\{\begin{matrix}3x+1=x+3\\-\left(3x+1\right)=x+3\end{matrix}\right.\Rightarrow\left\{\begin{matrix}3x-x=3-1\\-3x-1=x+3\end{matrix}\right.\)
\(\Rightarrow\left\{\begin{matrix}2x=2\\-3x-x=3+1\end{matrix}\right.\Rightarrow\left\{\begin{matrix}x=1\\-4x=4\end{matrix}\right.\)
\(\Rightarrow\left\{\begin{matrix}x=1\\x=-1\end{matrix}\right.\)
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a) \(\dfrac{-x}{4}=\dfrac{-9}{x}\)
\(\Rightarrow-x^2=-36\)
\(\Rightarrow x^2=36\)
\(\Rightarrow\left[{}\begin{matrix}x=6\\x=-6\end{matrix}\right.\)
Vậy: \(x\in\left\{6;-6\right\}\)
b) \(\dfrac{5}{9}+\dfrac{x}{-1}=-\dfrac{1}{3}\)
\(\Rightarrow\dfrac{5}{9}+\dfrac{-9x}{9}=\dfrac{-3}{9}\)
\(\Rightarrow5-9x=-3\)
\(\Rightarrow-9x=-8\)
\(\Rightarrow x=\dfrac{8}{9}\)
Vậy: \(x=\dfrac{8}{9}\)
c) \(x:3\dfrac{1}{5}=1\dfrac{1}{2}\)
\(\Rightarrow x:\dfrac{16}{5}=\dfrac{3}{2}\)
\(\Rightarrow x=\dfrac{3}{2}.\dfrac{16}{5}\)
\(\Rightarrow x=\dfrac{24}{5}\)
Vậy: \(x=\dfrac{24}{5}\)
d) \(\dfrac{3x-1}{-5}=\dfrac{-5}{3x-1}\)
\(\Rightarrow\left(3x-1\right)^2=25\)
\(\Rightarrow\left[{}\begin{matrix}3x-1=5\\3x-1=-5\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}3x=6\\3x=-4\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\x=-\dfrac{4}{3}\end{matrix}\right.\)
Vậy: \(x\in\left\{2;-\dfrac{4}{3}\right\}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) |2x - 1| - 3 = 5
=> |2x - 1| = 8
Có 2 TH xảy ra:
TH1 : 2x - 1 = 8 => 2x = 9 => x = 9/2 (ko thỏa mãn x thuộc Z)
TH2 : -(2x - 1) = 8 => -2x + 1 = 8 => -2x = 9 => x = -9/2 (ko thỏa mãn x thuộc Z)
b) |3x - 5| = 4
Có 2 TH xảy ra :
TH1 : 3x - 5 = 4 => 3x = 9 => x = 3
TH2 : -(3x - 5) = 4 => -3x + 5 = 4 => -3x = -1 => x = 1/3 (ko thỏa mãn x thuộc Z)
c) |5x - 1| = |-3 - 3x|
Có 2 TH xảy ra :
TH1 : 5x - 1 = -3 - 3x => 5x + 3x = -3 + 1 => 8x = -2 => x = -1/4 (ko thỏa mãn x thuộc Z)
TH2 : 5x - 1 = -(-3 - 3x) => 5x - 1 = 3 + 3x => 5x - 3x = 3 +1 => 2x = 4 => x = 2
d) |4x - 8| = |x + 1|
Có 2 TH xảy ra :
TH1 : 4x - 8 = x + 1 => 4x - x = 1 + 8 => 3x = 9 => x = 3
TH2 : 4x - 8 = -(x + 10) => 4x - 8 = -x - 10 => 4x + x = -10 + 8 => 5x = -2 => x = -2/5 (ko thỏa mãn x thuộc Z)
e) |3x - 5| - |4x + 9| = 0
=> |3x - 5| = |4x + 9|
Có 2 TH xảy ra :
TH1 : 3x - 5 = 4x + 9 => 3x - 4x = 9 + 5 => -x = 14 => x = -14
TH2 : 3x - 5 = -(4x + 9) => 3x - 5 = -4x - 9 => 3x + 4x = -9 + 5 => 7x = -4 => x = -4/7 (ko thỏa mãn x thuộc Z)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) -3x+4+5x=-10-x
-3x+4+5x+10+x=0
(-3x+5x+x)+10=0
3x+10=0
3x=-10
x=\(\dfrac{-10}{3}\)
Vậy x=\(\dfrac{-10}{3}\)
b)-x+1=-3x-8
-x+1+3x+8=0
(-x+3x)+(1+8)=0
2x+9=0
2x=-9
x=\(\dfrac{-9}{2}\)
Vậy x=\(\dfrac{-9}{2}\)
c)8-(x-1)=10+(x+5)
8-x+1=10+x+5
9-x=15+x
9-x-15-x=0
(9-15)-(x+x)=0
-6-2x=0
2x=-6
x=-3
Vậy x=-3
d)100+(x+7)-(-2x+3)=8+(x+100)
100+x+7+2x-3=8+x+100
(x+2x)+(100+7-3)=(8+100)+x
3x+104=108+x
3x+104-108-x=0
(3x-x)+(104-108)=0
2x-4=0
2x=4
x=2
Vậy x=2
e, \(\left|2x+5\right|=\left|x-1\right|\)
\(\Rightarrow\left\{{}\begin{matrix}2x+5=1-x\\2x+5=x-1\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}3x=-4\\x=-6\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=-\dfrac{4}{3}\\x=-6\end{matrix}\right.\)
g, \(\left|-x+4\right|=\left|-3x-8\right|\)
\(\Rightarrow\left\{{}\begin{matrix}-x+4=3x+8\\-x+4=-3x-8\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}-4x=4\\2x=-12\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=-1\\x=-6\end{matrix}\right.\)
h, \(\left|x+4\right|=\left|-3-8\right|\)
\(\Rightarrow\left|x+4\right|=\left|-11\right|=11\)
\(\Rightarrow\left\{{}\begin{matrix}x+4=-11\\x+4=11\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=-15\\x=7\end{matrix}\right.\)
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d) |3x-1| = |x+3|
Trường hợp 1: 3x-1 = x+3
=> 3x - x = 3 +1
=> 2x = 4
=> x= 2
Trường hợp 2: 3x-1 = -x-3
=> 3x+x= -3 +1
=> 4x = -2
=> x= -1/2
Vậy x =2 hoặc x =-1/2