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1)\(-\dfrac{4x-3}{x-5}=\dfrac{29}{3}\Leftrightarrow\dfrac{3-4x}{x-5}=\dfrac{29}{3}\)
\(\Leftrightarrow3\left(3-4x\right)=29\left(x-5\right)\Leftrightarrow9-12x=29x-145\)
\(\Leftrightarrow29x+12x=9+145\Leftrightarrow41x=154\Leftrightarrow x=\dfrac{154}{41}\)
2)\(\dfrac{2x-1}{5-3x}=2\Leftrightarrow2\left(2x-1\right)=5-3x\)
\(\Leftrightarrow4x-2=5-3x\)
\(\Leftrightarrow4x+3x=5+2\Leftrightarrow7x=7\Leftrightarrow x=1\)
3)\(\dfrac{4x-5}{x-1}=2+\dfrac{x}{x-1}\)
\(\Leftrightarrow\dfrac{4x-5}{x-1}=\dfrac{2\left(x-1\right)}{x-1}+\dfrac{x}{x-1}\)
\(\Rightarrow4x-5=2x-2+x\)
\(\Leftrightarrow4x-2x-x=-2+5\)
\(\Leftrightarrow x=3\)
\(1)-\dfrac{4x-3}{x-5}=\dfrac{29}{3} (x \neq 5) \\\Leftrightarrow\dfrac{3-4x}{x-5}=\dfrac{29}{3}\) \(\Leftrightarrow3\left(3-4x\right)=29\left(x-5\right)\\\Leftrightarrow9-12x=29x-145\) \(\Leftrightarrow29x+12x=9+145\\\Leftrightarrow41x=154\\\Leftrightarrow x=\dfrac{154}{41}(TM)\)
Vậy \(S=\left\{\dfrac{154}{41}\right\}\)
\(2)\dfrac{2x-1}{5-3x}=2 (x \neq \dfrac{5}{3}) \)
\(\Leftrightarrow2x-1=2\left(5-3x\right)\\ \Leftrightarrow2x-1=10-6x\\ \Leftrightarrow2x+6x=10+1\\ \Leftrightarrow8x=11\\ \Leftrightarrow x=\dfrac{11}{8}\left(TM\right)\)
Vậy \(S=\left\{\dfrac{11}{8}\right\}\)
\(3)\dfrac{4x-5}{x-1}=2+\dfrac{x}{x-1} (x \neq 1) \\\Leftrightarrow\dfrac{4x-5}{x-1}=\dfrac{2\left(x-1\right)}{x-1}+\dfrac{x}{x-1}\) \(\Leftrightarrow4x-5=2x-2+x\) \(\Leftrightarrow4x-2x-x=-2+5\) \(\Leftrightarrow x=3(TM)\)
Vậy \(S=\left\{3\right\}\)
Mấy này bạn quy đồng lên cùng mẫu xong khử mẫu rồi giải. Dễ mà.
a) \(\dfrac{5x-1}{3x+2}=\dfrac{5x-7}{3x-1}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta được:
\(\dfrac{5x-1}{3x+2}=\dfrac{5x-7}{3x-1}\)
\(=\dfrac{5x-1-5x+7}{3x+2-3x+1}\)
\(=\dfrac{-1+7}{2+1}\)
\(=\dfrac{6}{3}\)
\(=2\)
Với \(\dfrac{5x-1}{3x+2}=2\)
\(\Rightarrow5x-1=2\left(3x+2\right)\)
\(\Rightarrow5x-1-2\left(3x+2\right)=0\)
\(\Rightarrow5x-1-6x-4=0\)
\(\Rightarrow-x-5=0\)
\(\Rightarrow x=-5\)
a: =>-4x>16
=>x<-4
c: =>20x-25<=21-3x
=>23x<=46
=>x<=2
d: =>20(2x-5)-30(3x-1)<12(3-x)-15(2x-1)
=>40x-100-90x+30<36-12x-30x+15
=>-50x-70<-42x+51
=>-8x<121
=>x>-121/8
giải các phương trình sau:
a) 6x-3= 4x+5
b) \(\dfrac{2x+3}{x+1}\)- \(\dfrac{6}{x}\)= 2
c) \(|3x-1|\)=3x
a)\(6x-3=4x+5\)
\(\Rightarrow6x-3-4x-5=0\)
\(\Rightarrow2x-8=0\)
\(\Rightarrow x=4\)
Vậy x=4
b)\(\frac{2x+3}{x+1}-\frac{6}{x}=2\left(ĐKXĐ:x\ne-1;0\right)\)
\(\Rightarrow\frac{2x^2+3x}{x\left(x+1\right)}-\frac{6x+6}{x\left(x+1\right)}=2\)
\(\Rightarrow\frac{2x^2+3x-6x-6}{x\left(x+1\right)}=2\)
\(\Rightarrow2x^2-3x-6=2\left(x^2+x\right)\)
\(\Rightarrow2x^2-3x-6-2x^2-2x=0\)
\(\Rightarrow-5x-6=0\)
\(\Rightarrow x=-\frac{6}{5}\)
Vậy \(x=-\frac{6}{5}\)
c)\(\left|3x-1\right|=3x\left(1\right)\)
TH1:\(x\ge\frac{1}{3}\).PT(1) có dạng:3x-1=3x
0x=1
PT vô nghiệm
TH2:\(x< \frac{1}{3}\).PT(1) có dạng:1-3x=3x
\(\Rightarrow6x=1\)
\(\Rightarrow x=\frac{1}{6}\left(TM\right)\)
Vậy PT có nghiệm là \(\frac{1}{6}\)
a, \(6x-3=4x+5 \)
\(\Leftrightarrow6x-4x=5+3\)
\(\Leftrightarrow2x=8\)
\(\Leftrightarrow x=4\)
vậy no của pt là : x = 4
b, \(\frac{2x+3}{x+1}-\frac{6}{x}=2\)
ĐKXĐ : \(\hept{\begin{cases}x\ne-1\\x\ne0\end{cases}}\)
\(\Leftrightarrow\frac{2x^2+3x-6x-6}{x\left(x+1\right)}=2\)
\(\Leftrightarrow\frac{2x^2-3x-6}{x\left(x+1\right)}=2\)
\(\Leftrightarrow2x^2-3x-6=2x^2+2x\)
\(\Leftrightarrow-5x=6\)
\(\Leftrightarrow x=\frac{-6}{5}\)
vậy no của pt là x=-6/5
c, \(\left|3x-1\right|=3x\)
Với \(3x-1\ge0\)
\(\Rightarrow3x-1=3x\Leftrightarrow-1=0\)( vô lí )
\(\Leftrightarrow x\left(4x-3\right)-\left(x-2\right)\left(3x+2\right)=x^2-5\)
\(\Leftrightarrow4x^2-3x-3x^2-2x+6x+4=x^2-5\)
\(\Leftrightarrow x^2+x+4=x^2-5\)
=>x+4=-5
hay x=-9(nhận)