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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
\(\left(-\frac{2}{3}:-\frac{1}{3}\right).\left(-\frac{9}{2}\right)-\frac{1}{4}< \frac{x}{8}< -\frac{1}{2}.\frac{3}{4}:\frac{1}{8}+1\)
\(2.\left(-\frac{9}{2}\right)-\frac{1}{4}< \frac{x}{8}< \left(-3\right)+1\)
\(\left(-9\right)-\frac{1}{4}< \frac{x}{8}< \left(-2\right)\)
\(\left(-\frac{37}{4}\right)< \frac{x}{8}< \left(-2\right)\)
\(-\frac{74}{8}< \frac{x}{8}< -\frac{16}{8}\)
Vậy -74<x<-16
3/ Ta có:
\(A=\dfrac{1-2x}{x+3}\)
\(A=\dfrac{-2x+1}{x+3}\)
\(A=\dfrac{-2x-6+7}{x+3}\)
\(A=\dfrac{-2\left(x+3\right)+7}{x+3}\)
\(A=-2+\dfrac{7}{x+3}\)
A nguyên khi \(\dfrac{7}{x+3}\) nguyên
⇒ 7 ⋮ \(x+3\)
\(\Rightarrow x+3\inƯ\left(7\right)\)
\(\Rightarrow x+3\in\left\{1;-1;7;-7\right\}\)
\(\Rightarrow x\in\left\{-2;-4;4;-10\right\}\)
Câu a tự làm nhé
b, \(\frac{2x+3}{24}=\frac{3x-1}{32}\)
\(\Leftrightarrow32(2x+3)=24(3x-1)\)
\(\Leftrightarrow64x+96=72x-24\)
\(\Leftrightarrow64x+96-72x=-24\)
\(\Leftrightarrow96-8x=-24\Leftrightarrow x=15\)
Bài 2:
a: =>x=0 hoặc x=-3
b: =>x-2=0 hoặc 5-x=0
=>x=2 hoặc x=5
c: =>x-1=0
hay x=1
bài 1 : a,ta có 3/x-1 =4/y-2=5/z-3 => x-1/3=y-2/4=z-3/5
áp dụng .... => x-1+y-2+z-3 / 3+4+5 = x+y+z-1-2-3/3+4+5 = 12/12=1
do x-1/3 = 1 => x-1 = 3 => x= 4 ( tìm y,z tương tự
Bài 1:
a) Ta có: 3/x - 1 = 4/y - 2 = 5/z - 3 => x - 1/3 = y - 2/4 = z - 3/5 áp dụng ... =>x - 1 + y - 2 + z - 3/3 + 4 + 5 = x + y + z - 1 - 2 - 3/3 + 4 + 5 = 12/12 = 1 do x - 1/3 = 1 => x - 1 = 3 => x = 4 ( tìm y, z tương tự )
\(\dfrac{x-1}{2011}+\dfrac{x-2}{2010}-\dfrac{x-3}{2009}=\dfrac{x-4}{2008}\)
<=> \(\left(\dfrac{x-1}{2011}-1\right)+\left(\dfrac{x-2}{2010}-1\right)-\left(\dfrac{x-3}{2009}-1\right)=\left(\dfrac{x-4}{2008}-1\right)\)
<=> \(\dfrac{x-2012}{2011}+\dfrac{x-2012}{2010}-\dfrac{x-2012}{2009}-\dfrac{x-2012}{2008}=0\)
<=> \(\left(x-2012\right)\left(\dfrac{1}{2011}+\dfrac{1}{2010}-\dfrac{1}{2009}-\dfrac{1}{2008}\right)=0\)
<=> x - 2012 = 0
<=> x = 2012
`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`
Mình cảm ơn ạ!