a, / 2 +x / + / x-7 / = 3
b, / 13-x /+ / 6 -x / =7
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a) x : 1/6 = 3
x = 3 x 1/6
x = 1/2
b) 3/7 + x = 2/7 + 1
3/7 + x = 9/7
x = 9/7 - 3/7
x = 6/7
a: \(\dfrac{7}{x}-\dfrac{2}{6}-2>\dfrac{2\left(x+1\right)}{3}\)
=>\(\dfrac{7}{x}>\dfrac{2x+2}{3}+\dfrac{1}{3}+2=\dfrac{2x+2+1+6}{3}=\dfrac{2x+9}{3}\)
=>\(\dfrac{7}{x}-\dfrac{2x+9}{3}>0\)
=>\(\dfrac{21-2x^2-9x}{3x}>0\)
=>\(\dfrac{2x^2+9x-21}{x}< 0\)
TH1: x>0 và 2x^2+9x-21<0
=>x>0 và \(\dfrac{-9-\sqrt{249}}{4}< x< \dfrac{-9+\sqrt{249}}{4}\)
=>\(0< x< \dfrac{-9+\sqrt{249}}{4}\)
TH2: x<0 và 2x^2+9x-21>0
=>x<0 và (x<-9-căn 249)/4 hoặc (x>(-9+căn 249)/4))
=>x<(-9-căn 249)/4
a)4/9 : x/6 = 2/3
x/6 = 4/9 : 2/3
x/6 = 2/3 = 4/6
vậy x = 4
b)x/5 x 3/7 = 9/35
x/5 = 9/35 : 3/7
x/5 = 3/5
vậy x = 3
`1, -2/9 xx 15/17 + (-2/9) xx 2/17`
`= -2/9 xx (15/17 + 2/17)`
`= -2/9 xx 17/17`
`=-2/9xx1`
`=-2/9`
__
`-5/3 xx 6/5 + (-7/9) xx 3/10`
`= -30/15 + (-21/90)`
`= -2 + (-7/30)`
`=-60/30 +(-7/30)`
`=-67/30`
__
`15/20 xx 7/5 + (-9/7) xx (-6/4)`
`=3/4 xx7/5 + (-9/7) xx(-6/4)`
`= 21/20 + 54/28`
`= 21/20 + 27/14`
`=417/140`
__
`-25/13 xx 5/19 + (-25/13) xx 14/19`
`=-25/13 xx (5/19 +14/19)`
`=-25/13 xx 19/19`
`= -25/13 xx 1`
`=-25/13`
__
`-7/13 xx 13/5 + (-9/7) xx 5/3`
`=-7/5 +(-15/7)`
`=-124/35`
1: =-2/9(15/17+2/17)=-2/9
2: \(=\dfrac{-6}{3}+\dfrac{-21}{90}\)
=-2-7/30=-67/30
3: \(=\dfrac{3}{4}\cdot\dfrac{7}{5}+\dfrac{9}{7}\cdot\dfrac{3}{2}\)
=21/20+27/14=417/140
4: =-25/13(5/19+14/19)=-25/13
5: =-7/5-45/21=-7/5-15/7=-124/35
1: =-2/9(15/17+2/17)=-2/9
2: =−63+−2190=−63+−2190
=-2-7/30=-67/30
3: =34⋅75+97⋅32=34⋅75+97⋅32
=21/20+27/14=417/140
4: =-25/13(5/19+14/19)=-25/13
5: =-7/5-45/21=-7/5-15/7=-124/35
a).\(\dfrac{x}{15}\)=\(\dfrac{4}{3}\)\(\Leftrightarrow\)x.3=15.4\(\Leftrightarrow\)3x=60\(\Leftrightarrow\)x=20
b)x:\(\dfrac{4}{3}\)=\(\dfrac{5}{6}\)\(\Leftrightarrow\)\(\dfrac{3x}{4}=\dfrac{5}{6}\)\(\Leftrightarrow\)3x.6=4.5\(\Leftrightarrow\)18x=20\(\Leftrightarrow\)\(\dfrac{10}{9}\)
c)\(\dfrac{7}{2}\)-x=\(\dfrac{5}{6}\)\(\Leftrightarrow\)\(\dfrac{7}{2}-\dfrac{2x}{2}\)=\(\dfrac{5}{6}\)\(\Leftrightarrow\)\(\dfrac{7-2x}{2}\)=\(\dfrac{5}{6}\)\(\Leftrightarrow\)(7-2x).6=2.5\(\Leftrightarrow\)42-12x=10
\(\Leftrightarrow\)-12x=-32\(\Leftrightarrow\)x=\(\dfrac{8}{3}\)
a) |2+x|+|x-7|=3
Ta có: 2+x=0=>x=-2
x-7=0=>x=7
Lập bảng xét dấu:
x -2 7
2+x - 0 + +
x-7 - - 0 +
Nếu x<-2 thì: |2+x|= -(2+x)=-2-x
|x-7|=-(x-7)=-x+7
Khi đó: (-2-x)+(-x+7)=3
=> -2-x-x-7=3
=> -x-x=3+2+7
=> -2x= 12
=> x= -6( thỏa mãn x<-2)
Nếu -2\(\le\)x\(\le\)7 thì: |2+x|=2+x
|x-7|=-(x-7)=-x+7
Khi đó: (2+x)+(-x+7)=3
=> 2+x-x+7=3
=> +x-x=3-2-7
=> 0= -6 (Vô lý)
Nếu x>7 thì: |2+x|=2+x
|x-7|=x-7
Khi đó; (2+x)+(x-7)=3
=> 2+x+x+7=3
=> x+x=3-2-7
=> 2x=-6
=> x= -3( không thỏa mãn x>7)
Vậy x= -6