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`1/2-(1/3+3/4)<=x<=1/24-(1/8-1/3)`
`<=>6/12-4/12-9/12<=x<=1/24-3/24+8/24`
`<=>-7/12<=x<=1/4`
`<=>-14/24<=x<=3/12`
`=>-14<=x<=3`
`=>x\in{-14;-13;-12;...;3}` do `x\inZZ`
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có 1/2 - ( 1/3 + 3/4) <= x <= 1/24 - ( 1/8 - 1/3 )
=> 6/12 - ( 4/12 + 9/12 ) <= x <= 1/24 - ( 3/24 - 8/24 )
=> 6/12 - 13/12 <= x <= 1/24 + 5/24
=> -7/12 <= x <= 3/12
=> -7 <= 12x <= 3
=> x ko tồn tại
1/3– 3/5 + 5/7 –7/9 + 9/11 – 11/13 + 13/15 + 11/13 – 9/11 + 7/9 –5/7 + 3/5 –1/3
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\(\frac{1}{2}-\left\{\frac{1}{3}+\frac{3}{4}\right\}\)
\(=\frac{1}{2}-\frac{13}{12}\)
\(=\frac{1}{2}-1+\frac{1}{12}\)
\(=\frac{7}{12}-1\)
\(\frac{1}{2}-\left(\frac{1}{3}+\frac{3}{4}\right)\)
\(=\frac{1}{2}-\frac{13}{12}\)
\(=\frac{-7}{12}\)
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1, \(\left(x+7\right)\left(3x-1\right)=49-x^2\)
\(\Leftrightarrow\left(x+7\right)\left(3x-1\right)=\left(7-x\right)\left(7+x\right)\)
\(\Leftrightarrow3x-1=7-x\)
\(\Leftrightarrow4x=8\Leftrightarrow x=2\)
Vậy x = 2
2, \(\left(2x+1\right)^2-\left(x-1\right)^2=0\)
\(\Leftrightarrow\left(2x+1-x+1\right)\left(2x+1+x-1\right)=0\)
\(\Leftrightarrow\left(x+2\right)2x=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+2=0\\2x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=0\end{matrix}\right.\)
Vậy x = -2 hoặc x = 0
3, \(\left(1-2x\right)^2-\left(x+3\right)^2+3\left(x+1\right)\left(1-x\right)=8\)
\(\Leftrightarrow\left(1-2x-x-3\right)\left(1-2x+x+3\right)+3\left(x-x^2+1-x\right)=8\)
\(\Leftrightarrow\left(-2-3x\right)\left(4-x\right)-3x^2+3=8\)
\(\Leftrightarrow-8+2x-12x+3x^2-3x^2=5\)
\(\Leftrightarrow-10x=13\)
\(\Leftrightarrow x=-1,3\)
Vậy x = -1,3
4, \(\left(x-3\right)^2-\left(x+3\right)^2=24\)
\(\Leftrightarrow\left(x-3-x-3\right)\left(x-3+x+3\right)=24\)
\(\Leftrightarrow-6.2x=24\)
\(\Leftrightarrow x=-2\)
Vậy x = -2
![](https://rs.olm.vn/images/avt/0.png?1311)
1/2 - (1/3 + 3/4) < x < 1/24 - (1/8 - 1/3)
Ta có:
* 1/2 - (1/3 + 3/4) = 1/2 - 13/12
= -7/12. (1)
* 1/24 - (1/8 - 1/3) = 1/24 - 1/8 + 1/3
= 1/24 - 3/24 + 8/24
= 6/24 = 3/12 (2)
Từ (1) và (2) suy ra: x thuộc: {-1/2; -5/12; -1/3; -1/4; -1/6; -1/12; 0; 1/2; 1}.
![](https://rs.olm.vn/images/avt/0.png?1311)
a) 3/4 + -1/8 = 5/8
b)-5/12 + -7/24 = -9/8
c) 4/21 - -5/28 = 31/84
d) 1 + -7/28 = 3/4
e) -4/3 - 17/6= -25/6
f) 1/3 - ( 1/2 +1/8 )= -7/24
g)1/21 - ( 1/7 - 1/3 ) = 5/21
h)1/2 - 1/4 + 1/13 + 1/8= 47/104
a) x - 1/10 = 1/15
x=1/15+1/10
x=1/6 Vay x=1/6b) -4/21 - x = -3/7
x=-4/21+3/7 x=5/21 Vay x=5/21c) x + 1/2 = 3/4 - (-1/2)
x+1/2= 5/4
x= 5/4-1/2
x=3/4
Vay x=3/4
d) 4/7 - x = 1/3 - (-2/3)
x= 4/7-1/3-2/3 x= -3/7 Vay x=-3/7