tìm x:
1) \(\frac{x-4}{12}=\frac{x-6}{11}\)
2)\(\frac{3x+2}{-7}=\frac{x-4}{-2}\)
3)\(\frac{1-4x}{5}=\frac{2x-1}{-3}\)
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#)Giải :
a) x + 2x + 3x + ... + 100x = - 213
=> 100x + ( 2 + 3 + 4 + ... + 100 ) = - 213
=> 100x + 5049 = - 213
<=> 100x = - 5262
<=> x = - 52,62
#)Giải :
b) \(\frac{1}{2}x-\frac{1}{3}=\frac{1}{4}x-\frac{1}{6}\)
\(\Rightarrow\frac{1}{2}x+\frac{1}{4}x=\frac{1}{3}+\frac{1}{6}\)
\(\Rightarrow\frac{1}{2}x+\frac{1}{4}x=\frac{1}{2}\)
\(\Rightarrow\left(\frac{1}{2}+\frac{1}{4}\right)x=\frac{1}{2}\)
\(\Rightarrow\frac{3}{4}x=\frac{1}{2}\)
\(\Leftrightarrow x=\frac{2}{3}\)
\(\frac{3x-7}{5}=\frac{2x-1}{3}\)
\(\Leftrightarrow9x-21=10x-5\)
\(\Leftrightarrow-x=16\Leftrightarrow x=-16\)
\(\frac{4x-7}{12}-x=\frac{3x}{8}\)
\(\Leftrightarrow\frac{4x-7-12x}{12}=\frac{3x}{8}\)
\(\Leftrightarrow\frac{-7-8x}{12}=\frac{3x}{8}\)
\(\Leftrightarrow-56-64x=36x\)
\(\Leftrightarrow-56=100x\Leftrightarrow x=\frac{-14}{25}\)
\(\frac{x-2009}{1234}+\frac{x-2009}{5678}-\frac{x-2009}{197}=0\)
\(\Leftrightarrow\left(x-2019\right)\left(\frac{1}{1234}+\frac{1}{5678}-\frac{1}{197}\right)=0\)
Vì \(\left(\frac{1}{1234}+\frac{1}{5678}-\frac{1}{197}\right)\ne0\)nên x - 2019 = 0
Vậy x = 2019
\(\frac{5x-8}{3}=\frac{1-3x}{2}\)
\(\Leftrightarrow10x-16=3-9x\)
\(\Leftrightarrow19x=19\Leftrightarrow x=1\)
d: =>4x+6=15x-12
=>4x-15x=-12-6=-18
=>-11x=-18
hay x=18/11
e: =>\(45x+27=12+24x\)
=>21x=-15
hay x=-5/7
f: =>35x-5=96-6x
=>41x=101
hay x=101/41
g: =>3(x-3)=90-5(1-2x)
=>3x-9=90-5+10x
=>3x-9=10x+85
=>-7x=94
hay x=-94/7
a) 4 ( x + 5 )( x + 6 )( x + 10 )( x + 12 ) = 3x2
Do x = 0 không là nghiệm pt nên chia 2 vế pt cho \(x^2\ne0\), ta được :
\(\frac{4}{x^2}\left(x^2+60+17x\right)\left(x^2+60+16x\right)=3\)
\(\Leftrightarrow4\left(x+\frac{60}{x}+17\right)\left(x+\frac{60}{x}+16\right)=3\)
Đến đây ta đặt \(x+\frac{60}{x}+16=t\left(1\right)\)
Ta được :
\(4t\left(t+1\right)=3\Leftrightarrow4t^2+4t-3=0\Leftrightarrow\left(2t+3\right)\left(2t-1\right)=0\)
Từ đó ta lắp vào ( 1 ) tính được x
a, \(\frac{x-4}{12}=\frac{x-6}{11}\)
\(\Rightarrow11\left(x-4\right)=12\left(x-6\right)\)
\(\Rightarrow11x-44=12x-72\)
\(\Rightarrow11x-12x=-72+44\)
\(\Rightarrow-x=-28\)
=> x = 28
b, \(\frac{3x+2}{-7}=\frac{x-4}{-2}\)
\(\Rightarrow-2\left(3x+2\right)=-7\left(x-4\right)\)
\(\Rightarrow-6x+\left(-4\right)=-7x-\left(-28\right)\)
\(\Rightarrow-6x+\left(-4\right)=-7x+28\)
\(\Rightarrow-6x+7x=28-\left(-4\right)\)
\(\Rightarrow x=32\)
c, \(\frac{1-4x}{5}=\frac{2x-1}{-3}\)
\(\Rightarrow-3\left(1-4x\right)=5\left(2x-1\right)\)
\(\Rightarrow-3-\left(-12x\right)=10x-5\)
\(\Rightarrow-3+12x=10x-5\)
\(\Rightarrow-3+5=10x-12x\)
\(\Rightarrow2=-2x\)
=> x = 2 : (-2)
=> x = -1
1) X=28
2) X=32
3) X=-1