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\(\dfrac{x}{-3}=\dfrac{y}{5}\)⇒\(\dfrac{x}{-6}=\dfrac{y}{10}\)
\(\dfrac{y}{2}=\dfrac{z}{7}\)⇒\(\dfrac{y}{10}=\dfrac{z}{35}\)
⇒\(\dfrac{x}{-6}=\dfrac{y}{10}=\dfrac{z}{35}\)
⇒\(\dfrac{2x}{-12}=\dfrac{3y}{30}=\dfrac{z}{35}\)
Áp dụng tính chất dãy tỉ số bằng nhau, ta có:
\(\dfrac{2x}{-12}=\dfrac{3y}{30}=\dfrac{z}{35}=\dfrac{2x-3y+z}{-12-30+35}=\dfrac{42}{-7}=-6\)
⇒\(\left\{{}\begin{matrix}x=-6.-6=36\\y=-6.10=-60\\z=-6.35=-210\end{matrix}\right.\)
\(a,\dfrac{x}{-3}=\dfrac{y}{5}\Rightarrow\dfrac{x}{-6}=\dfrac{y}{10};\dfrac{y}{2}=\dfrac{z}{7}\Rightarrow\dfrac{y}{10}=\dfrac{z}{35}\\ \Rightarrow\dfrac{x}{-6}=\dfrac{y}{10}=\dfrac{z}{35}\)
Áp dụng t/c dtsbn:
\(\dfrac{x}{-6}=\dfrac{y}{10}=\dfrac{z}{35}=\dfrac{2x}{-12}=\dfrac{3y}{30}=\dfrac{2x-3y+z}{-12-30+35}=\dfrac{42}{-7}=-6\\ \Rightarrow\left\{{}\begin{matrix}x=36\\y=-60\\z=-210\end{matrix}\right.\)
\(b,6x=4y=z\Rightarrow\dfrac{6x}{12}=\dfrac{4y}{12}=\dfrac{z}{12}\Rightarrow\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{12}\)
Áp dụng t/c dtsbn:
\(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{12}=\dfrac{2x}{4}=\dfrac{3y}{9}=\dfrac{2x-3y+z}{4-9+12}=\dfrac{42}{7}=6\\ \Rightarrow\left\{{}\begin{matrix}x=12\\y=18\\z=72\end{matrix}\right.\)
\(c,x=-2y\Rightarrow\dfrac{x}{-2}=y\Rightarrow\dfrac{x}{-4}=\dfrac{y}{2}\\ 7y=2z\Rightarrow\dfrac{y}{2}=\dfrac{z}{7}\\ \Rightarrow\dfrac{x}{-4}=\dfrac{y}{2}=\dfrac{z}{7}\)
Áp dụng t/c dtsbn:
\(\dfrac{x}{-4}=\dfrac{y}{2}=\dfrac{z}{7}=\dfrac{2x}{-8}=\dfrac{3y}{6}=\dfrac{2x-3y+z}{-8+6+7}=\dfrac{42}{5}\\ \Rightarrow\left\{{}\begin{matrix}x=-\dfrac{168}{5}\\y=\dfrac{84}{5}\\z=\dfrac{294}{5}\end{matrix}\right.\)
\(a,\left|2x-5\right|=1\)
\(\Rightarrow\orbr{\begin{cases}2x-5=1\\2x-5=-1\end{cases}\Rightarrow\orbr{\begin{cases}2x=6\\2x=4\end{cases}\Rightarrow}\orbr{\begin{cases}x=3\\x=2\end{cases}}}\)
b, đề thiếu
a) |x - 1,7| = 2,3
Xét 2 trường hợp:
TH1: x - 1,7 = -2,3
x = -2,3 +1,7
x = -0,6
TH2: x - 1,7 = 2,3
x = 2,3 + 1,7
x = 4
Vậy: Tự kl :<
`|2x+1|-3=x+4`
`<=>|2x+1|=x+4+3=x+7(x>=-7)`
`**2x+1=x+7`
`<=>x=7-1=6(tm)`
`**2x+1=-x-7`
`<=>3x=-6`
`<=>x=-2(tm)`
`|3x-5|=1-3x(x<=1/3)`
`**3x-5=1-3x`
`<=>6x=6`
`<=>x=1(l)`
`**3x-5=3x-1`
`<=>-5=-1` vô lý
`|2x+2|+|x-1|=10`
Nếu `x>=1`
`pt<=>2x+2+x-1=10`
`<=>3x+1=10`
`<=>3x=9`
`<=>x=3(tm)`
Nếu `x<=-1`
`pt<=>-2x-2+1-x=10`
`<=>-1-3x=10`
`<=>-11=3x`
`<=>x=-11/3(tm)`
Nếu `-1<=x<=1`
`pt<=>2x+2+1-x=10`
`<=>x+3=10`
`<=>x=7(l)`
Vậy `S={3,-11/3}`
280 - ( x - 140 ) : 35 = 270
<=> ( x - 140 ) : 35 = 280 -270
<=> ( x -140 ) : 35 = 10
<=> x -140 = 10 . 35
<=> x -140 = 350
<=> x = 350 + 140
<=> x = 490
1) 280 - ( x - 140 ) : 35 = 270
=> ( x - 140 ) : 35 = 280 - 270 = 10
x - 140 = 350
=> x = 350 + 140
=> x = 390
2) ( 190 - 2x ) : 35 - 32 = 16
190 - 2x = ( 16 + 32 ) . 35 = 1680
x = ( 190 - 1680 ) : 2
x = -745
3) 720 : { 41 - ( 2x - 5 )} -2.5
Sai đề.
4) ( x : 23 + 45 ) . 37 - 22 = 24 .105
x : 23 + 45 = ( 24.105 + 22 ) : 37
x : 23 = 2542/37 - 45 = 877/37
x = 877/37.23 = 20171/37
5) ( 3x - 4 ) ( x - 1 ) = 0
=> 3x - 4 = 0 hoặc x - 1 = 0
3x - 4 = 0 hoặc x - 1 = 0
=> x = 4/3 => x = 1
Vậy x \(\in\) { 4/3;1 }
6) 22x : 4 = 83
=> 22x = 83 . 4 = 2048 = 211
=> 2x = 11
=> x = 11/2
\(\left(x+\frac{2}{3}\right)\left(\frac{5}{4}-2x\right)>0\)
th1 :
\(\hept{\begin{cases}x+\frac{2}{3}>0\\\frac{5}{4}-2x>0\end{cases}\Rightarrow\hept{\begin{cases}x>-\frac{2}{3}\\-2x>-\frac{5}{4}\end{cases}\Rightarrow}\hept{\begin{cases}x>-\frac{2}{3}\\x>\frac{5}{8}\end{cases}\Rightarrow}x>\frac{5}{8}}\)
th2 :
\(\hept{\begin{cases}x+\frac{2}{3}< 0\\\frac{5}{4}-2x< 0\end{cases}\Rightarrow\hept{\begin{cases}x< -\frac{2}{3}\\-2x< -\frac{5}{4}\end{cases}\Rightarrow}\hept{\begin{cases}x< -\frac{2}{3}\\x< \frac{5}{8}\end{cases}\Rightarrow}x< -\frac{2}{3}}\)
vậy_
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) \(3x\left(2x-5\right)-15\left(5-2x\right)=0\)
\(\Leftrightarrow3\left[x\left(2x-5\right)-5\left(5-2x\right)\right]=0\)
\(\Leftrightarrow x\left(2x-5\right)-5\left(5-2x\right)=0\)
\(\Leftrightarrow\left(x+5\right)\left(2x-5\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x+5=0\\2x-5=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=-5\\x=\frac{5}{2}\end{cases}}\)
a,575-(6x+70)=445
<=> 6x + 70 = 575 - 445
<=> 6x + 70 = 130
<=> 6x = 130 - 70
<=> 6x = 60
<=> x = 10
b, 720 : [ 41 - ( 2x - 5 ) ]= 23. 5
<=> 720 : [ 41 - ( 2x - 5 ) ] = 40
<=> 41 - ( 2x - 5 ) = 18
<=> 2x - 5 = 41 - 18
<=> 2x - 5 = 23
<=> 2x = 28
<=> x = 14
a) 6x+70 = 575 - 445
6x+70= 130
6x = 130 - 70
6x = 60
x =60 : 6
x =10