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a. 3(x-2)-10=5(2x + 1)
<=> 3x - 6 - 10 = 10x + 5
<=> 3x - 10x = 5 + 6 + 10
<=> -7x = 21
<=> x = -3
b. 3x + 2=8 -2(x-7)
<=> 3x + 2 = 8 - 2x + 14
<=> 3x + 2x = 8 + 14 - 2
<=> 5x = 20
<=> x = 4
c. 2x-(2+5x)= 4(x + 3)
<=> 2x - 2 - 5x = 4x + 12
<=> 2x - 5x - 4x = 12 + 2
<=> -7x = 14
<=> x = -2
d. 5-(x +8)=3x + 3(x-9)
<=> 5 - x - 8 = 3x + 3x - 27
<=> -x - 3x - 3x = -27 + 8 - 5
<=> -7x = -24
<=> x = 24/7
e. 3x - 18 + x= 12-(5x + 3)
<=> 3x - 18 + x = 12 - 5x - 3
<=> 3x + x - 5x = 12 - 3 + 18
<=> -x = 27
<=> x = - 27
a. 3(x-2)-10=5(2x + 1)
<=> 3x - 6 - 10 = 10x + 5
<=> 3x - 10x = 5 + 6 + 10
<=> -7x = 21
<=> x = -3
b. 3x + 2=8 -2(x-7)
<=> 3x + 2 = 8 - 2x + 14
<=> 3x + 2x = 8 + 14 - 2
<=> 5x = 20
<=> x = 4
c. 2x-(2+5x)= 4(x + 3)
<=> 2x - 2 - 5x = 4x + 12
<=> 2x - 5x - 4x = 12 + 2
<=> -7x = 14
<=> x = -2
d. 5-(x +8)=3x + 3(x-9)
<=> 5 - x - 8 = 3x + 3x - 27
<=> -x - 3x - 3x = -27 + 8 - 5
<=> -7x = -24
<=> x = 24/7
e. 3x - 18 + x= 12-(5x + 3)
<=> 3x - 18 + x = 12 - 5x - 3
<=> 3x + x - 5x = 12 - 3 + 18
<=> -x = 27
<=> x = - 27
\(e,4\left(x-3\right)^2-\left(2x-1\right)\left(2x+1\right)=10\)
\(\Leftrightarrow4\left(x^2-6x+9\right)-\left(4x^2-1\right)=10\)
\(\Leftrightarrow4x^2-24x+36-4x^2+1=10\)
\(\Leftrightarrow-24x+37=10\)
\(\Leftrightarrow-24x=-27\)
\(\Leftrightarrow x=\dfrac{9}{8}\)
\(f,25\left(x+3\right)^2+ \left(1-5x\right)\left(1+5x\right)=8\)
\(\Leftrightarrow25\left(x^2+6x+9\right)+\left(1-25x^2\right)=8\)
\(\Leftrightarrow25x^2+150x+225+1-25x^2=8\)
\(\Leftrightarrow150x+226=8\)
\(\Leftrightarrow150x=-218\)
\(\Leftrightarrow x=-\dfrac{109}{75}\)
\(g,9\left(x+1\right)^2-\left(3x-2\right)\left(3x+2\right)=10\)
\(\Leftrightarrow9\left(x^2+2x+1\right)-\left(9x^2-4\right)=10\)
\(\Leftrightarrow9x^2+18x+9-9x^2+4=10\)
\(\Leftrightarrow18x+13=10\)
\(\Leftrightarrow18x=-3\)
\(\Leftrightarrow x=-\dfrac{1}{6}\)
\(h,-4\left(x-1\right)^2+\left(2x-1\right)\left(2x+1\right)=-3\)
\(\Leftrightarrow-4\left(x^2-2x+1\right)+\left(4x^2-1\right)=-3\)
\(\Leftrightarrow-4x^2+8x-4+4x^2-1=-3\)
\(\Leftrightarrow8x-5=-3\)
\(\Leftrightarrow8x=2\)
\(\Leftrightarrow x=\dfrac{1}{4}\)
#\(Toru\)
c) \(\dfrac{x}{x-2}+\dfrac{x}{x+2}=\dfrac{4x}{x^2-4}.ĐKXĐ:x\ne2;-2\)
<=>\(\dfrac{x\left(x+2\right)}{x^2-4}+\dfrac{x\left(x-2\right)}{x^2-4}=\dfrac{4x}{x^2-4}\)
<=>x2+2x+x2-2x=4x
<=>2x2-4x=0
<=>2x(x-2)=0
<=>\(\left[{}\begin{matrix}2x=0< =>x=0\\x-2=0< =>x=2\left(loại\right)\end{matrix}\right.\)
Vậy pt trên có nghiệm là S={0}
d) 11x-9=5x+3
<=>11x-5x=9+3
<=>6x=12
<=>x=2
Vậy pt trên có nghiệm là S={2}
e) (2x+3)(3x-4) =0
<=> \(\left[{}\begin{matrix}2x+3=0< =>x=\dfrac{-3}{2}\\3x-4=0< =>x=\dfrac{4}{3}\end{matrix}\right.\)
Vậy pt trên có tập nghiệm là S={\(\dfrac{-3}{2};\dfrac{4}{3}\)}
a) 5x+9 =2x
<=> 5x-2x=9
<=> 3x=9
<=> x=3
Vậy pt trên có nghiệm là S={3}
b) (x+1)(4x-3)=(2x+5)(x+1)
<=> (x+1)(4x-3)-(2x+5)(x+1)=0
<=>(x+1)(2x-8)=0
<=>\(\left[{}\begin{matrix}x+1=0< =>x=-1\\2x-8=0< =>2x=8< =>x=4\end{matrix}\right.\)
Vậy pt trên có tập nghiệm là S={-1;4}
1: Ta có: \(\dfrac{-3}{x-4}-\dfrac{3-5x}{x^2-16}=\dfrac{1}{x+4}\)
Suy ra: \(-3\left(x+4\right)-3+5x=x-4\)
\(\Leftrightarrow-3x-12-3+5x-x+4=0\)
\(\Leftrightarrow x=11\left(nhận\right)\)
2. ĐKXĐ: $x\neq \pm 2$
PT \(\Leftrightarrow \frac{3(x-2)}{(2+x)(x-2)}-\frac{x-1}{(x-2)(x+2)}=\frac{2(x+2)}{(x-2)(x+2)}\)
\(\Leftrightarrow \frac{3(x-2)-(x-1)}{(x-2)(x+2)}=\frac{2(x+2)}{(x-2)(x+2)}\)
\(\Rightarrow 3(x-2)-(x-1)=2(x+2)\)
\(\Leftrightarrow 2x-5=2x+4\Leftrightarrow 9=0\) (vô lý)
Vậy pt vô nghiệm
a: =>3,6-1,7x=2,3-1,4-4=0,9-4=-3,1
=>1,7x=6,7
hay x=67/17
b: \(\Leftrightarrow30\left(5x+4\right)-15\left(3x+5\right)=24\left(4x+9\right)-40\left(x-9\right)\)
=>150x+120-45x-75=96x+216-40x+360
=>105x+45=56x+576
=>49x=531
hay x=531/49
a, \(\left(x-2\right)^2-\left(x-3\right)\left(x+3\right)=6\) \(\Rightarrow x^2-4x+4-\left(x^2-9\right)=6\)
\(\Rightarrow x^2-4x+4-x^2+9=6\) \(\Rightarrow13-4x=6\Rightarrow4x=7\Rightarrow x=\frac{7}{4}\)
b, \(9.\left(x+1\right)^2-\left(3x-2\right)\left(3x+2\right)=10\)
\(\Rightarrow9\left(x^2+2x+1\right)-\left[\left(3x\right)^2-2^2\right]=10\)
\(\Rightarrow9x^2+18x+9-9x^2+4=10\) \(\Rightarrow18x+13=10\Rightarrow18x=-3\Rightarrow x=\frac{-3}{18}\)
c, \(\left(x+3\right)^2+\left(4+x\right)\left(4-x\right)=10\)
\(\Rightarrow x^2+6x+9+4^2-x^2=10\) \(\Rightarrow6x+25=10\Rightarrow6x=-15\Rightarrow x=\frac{-15}{6}\)
d, \(25\left(x+3\right)^2+\left(1-5x\right)\left(1+5x\right)=8\)
\(\Rightarrow25.\left(x^2+6x+9\right)+1^2-\left(5x\right)^2=10\)
\(\Rightarrow25x^2+150x+225+1-25x^2=10\)
\(\Rightarrow150x+226=10\Rightarrow150x=-216\Rightarrow x=\frac{-36}{25}\)
e, \(-4\left(x-1\right)^2+\left(2x-1\right)\left(2x+1\right)=-3\)
\(\Rightarrow-4\left(x^2-2x+1\right)+4x^2-1=-3\)
\(\Rightarrow-4x^2+8x-4+4x^2-1=-3\)
\(\Rightarrow8x-5=-3\Rightarrow8x=-2\Rightarrow x=\frac{-1}{4}\)