a) \(5x-2=3x+8\)
\(\Leftrightarrow5x-3x=8+2\)
\(\Leftrightarrow2x=10\)
\(\Leftrightarrow x=5\)
Vậy S = {5}
b) \(\dfrac{x+1}{2}+\dfrac{3x-2}{3}=\dfrac{x-7}{12}\)
\(\Leftrightarrow\dfrac{6\left(x+1\right)}{12}+\dfrac{4\left(3x-2\right)}{12}=\dfrac{x-7}{12}\)
\(\Leftrightarrow6x+6+12x-8=x-7\)
\(\Leftrightarrow6x+12x-x=-7-6+8\)
\(\Leftrightarrow17x=-5\)
\(\Leftrightarrow x=-\dfrac{5}{17}\)
Vậy \(S=\left\{-\dfrac{5}{17}\right\}\)
c) \(\left(x-4\right)\left(7x-3\right)-x^2+16=0\)
\(\Leftrightarrow7x^2-3x-28x+12-x^2+16=0\)
\(\Leftrightarrow6x^2-31x+28=0\)
\(\Leftrightarrow6x^2-24x-7x+28=0\)
\(\Leftrightarrow\left(6x^2-24x\right)-\left(7x-28\right)=0\)
\(\Leftrightarrow6x\left(x-4\right)-7\left(x-4\right)=0\)
\(\Leftrightarrow\left(x-4\right)\left(6x-7\right)=0\)
\(\Leftrightarrow x-4=0;6x-7=0\)
*) \(x-4=0\)
\(\Leftrightarrow x=4\)
*) \(6x-7=0\)
\(\Leftrightarrow6x=7\)
\(\Leftrightarrow x=\dfrac{7}{6}\)
Vậy \(S=\left\{\dfrac{7}{6};4\right\}\)
d) \(\dfrac{2x}{x-3}-\dfrac{5}{x+3}=\dfrac{x^2+21}{x^2-9}\) (1)
ĐKXĐ: \(x\ne3;x\ne-3\)
MTC: \(x^2-9\)
\(\left(1\right)\Leftrightarrow2x\left(x+3\right)-5\left(x-3\right)=x^2+21\)
\(\Leftrightarrow2x^2+6x-5x+15-x^2-21=0\)
\(\Leftrightarrow x^2+x-6=0\)
\(\Leftrightarrow x^2+2x-3x-6=0\)
\(\Leftrightarrow\left(x^2+2x\right)-\left(3x+6\right)=0\)
\(\Leftrightarrow x\left(x+2\right)-3\left(x+2\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(x-3\right)=0\)
\(\Leftrightarrow x+2=0;x-3=0\)
*) \(x+2=0\)
\(x=-2\) (nhận)
*) \(x-3=0\)
\(x=3\) (loại)
Vậy \(S=\left\{-2\right\}\)
a: =>5x-3x=8+2
=>2x=10
hay x=5
b: =>6(x+1)+4(3x-2)=x-7
=>6x+6+12x-8-x+7=0
=>17x=-5
hay x=-5/17
c: =>(x-4)(7x-3-x-4)=0
=>(x-4)(6x-7)=0
=>x=4 hoặc x=7/6
d: Suy ra: 2x(x+3)-5(x-3)=x2+21
\(\Leftrightarrow2x^2+6x-5x+15-x^2-21=0\)
\(\Leftrightarrow x^2+x-6=0\)
=>(x+3)(x-2)=0
=>x=2
