a: =>|x-7|=3-2x

\(\Leftrightarrow\left\{{}\begin{matrix}x< =\dfrac{3}{2}\\\left(-2x+3\right)^2-\left(x-7\right)^2=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x< =\dfrac{3}{2}\\\left(2x-3-x+7\right)\left(2x-3+x-7\right)=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x< =\dfrac{3}{2}\\\left(x+4\right)\left(3x-10\right)=0\end{matrix}\right.\Leftrightarrow x=-4\)

b: =>|2x-3|=4x+9

\(\Leftrightarrow\left\{{}\begin{matrix}x>=-\dfrac{9}{4}\\\left(4x+9-2x+3\right)\left(4x+9+2x-3\right)=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x>=-\dfrac{9}{4}\\\left(2x+12\right)\left(6x+6\right)=0\end{matrix}\right.\Leftrightarrow x=-1\)

c: =>3x+5=2-5x hoặc 3x+5=5x-2

=>8x=-3 hoặc -2x=-7

=>x=-3/8 hoặc x=7/2

a)(2x+1)(3x-2)=(5x-8)(2x+1)

⇔(2x+1)(3x-2)-(5x-8)(2x+1)=0

⇔(2x+1)(3x-2-5x+8)=0

⇔(2x+1)(-2x+6)=0

⇔2x+1=0 hoặc -2x+6=0

1.2x+1=0⇔2x=-1⇔x=-1/2

2.-2x+6=0⇔-2x=-6⇔x=3

phương trình có 2 nghiệm x=-1/2 và x=3

b)4x²-1=(2x+1)(3x-5)

⇔(2x-1)(2x+1)-(2x+1)(3x-5)=0

⇔(2x+1)(2x-1-3x+5)=0

⇔(2x+1)(-x+4)=0

⇔2x+1=0 hoặc -x+4=0

1.2x+1=0⇔2x=-1⇔x=-1/2

2.-x+4=0⇔-x=-4⇔x=4

phương trình có 2 nghiệm x=-1/2 và x=4

\(a,\left|2x\right|=x-6\)

\(\Leftrightarrow2x=x-6\)

\(\Leftrightarrow2x-x=-6\)

\(\Leftrightarrow x=-6\)

____________________

\(b,\left|-3x\right|=x-8\)

\(\Leftrightarrow3x=x-8\)

\(\Leftrightarrow3x-x=-8\)

\(\Leftrightarrow2x=-8\)

\(\Leftrightarrow x=-4\)

____________________

\(c,\left|4x\right|=2x+12\)

\(\Leftrightarrow4x=2x+12\)

\(\Leftrightarrow4x-2x=12\)

\(\Leftrightarrow2x=12\)

\(\Leftrightarrow x=6\)

____________________

\(d,\left|-5x\right|-16=3x\)

\(\Leftrightarrow5x-16=3x\)

\(\Leftrightarrow5x-3x=16\)

\(\Leftrightarrow2x=16\)

\(\Leftrightarrow x=8\)

a: =>x+3=x-2 hoặc x+3=2-x

=>2x=-1

=>x=-1/2

b: =>3x+7=x-2 hoặc 3x+7=-x+2

=>2x=-9 hoặc 4x=-5

=>x=-5/4 hoặc x=-9/2

c: =>|3x-4|=|2x-5|

=>3x-4=2x-5 hoặc 3x-4=-2x+5

=>x=-1 hoặc x=9/5

a: \(log\left(x-5\right)< 2\)

=>\(\left\{{}\begin{matrix}x-5>0\\log\left(x-5\right)< log4\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x-5>0\\x-5< 4\end{matrix}\right.\Leftrightarrow5< x< 9\)

b: \(log_2\left(2x-3\right)>4\)

=>\(log_2\left(2x-3\right)>log_216\)

=>\(\left\{{}\begin{matrix}2x-3>0\\2x-3>16\end{matrix}\right.\)

=>2x-3>16

=>2x>19

=>\(x>\dfrac{19}{2}\)

c: \(log_3\left(2x+5\right)< =3\)

=>\(log_3\left(2x+5\right)< =log_327\)

=>\(\left\{{}\begin{matrix}2x+5>0\\2x+5< =27\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x>-\dfrac{5}{2}\\x< =11\end{matrix}\right.\)

=>\(-\dfrac{5}{2}< x< =11\)

d: \(log_4\left(4x-5\right)>=2\)

=>\(log_4\left(4x-5\right)>=log_416\)

=>4x-5>=16 và 4x-5>0

=>4x>=21 và 4x>5

=>4x>=21

=>\(x>=\dfrac{21}{4}\)

e: \(log_3\left(1-3x\right)>3\)

=>\(log_3\left(1-3x\right)>log_327\)

=>\(\left\{{}\begin{matrix}1-3x>0\\1-3x>27\end{matrix}\right.\)

=>1-3x>27

=>\(-3x>26\)

=>\(x< -\dfrac{26}{3}\)

a) Ta có: \(\sqrt{25x+75}+3\sqrt{x-2}=2\sqrt{x-2}+\sqrt{9x-18}\)

\(\Leftrightarrow5\sqrt{x+3}+3\sqrt{x-2}=2\sqrt{x-2}+3\sqrt{x-2}\)

\(\Leftrightarrow\sqrt{25x+75}=\sqrt{4x-8}\)

\(\Leftrightarrow25x-4x=-8-75\)

\(\Leftrightarrow21x=-83\)

hay \(x=-\dfrac{83}{21}\)

b) Ta có: \(\sqrt{\left(2x-1\right)^2}=4\)

\(\Leftrightarrow\left|2x-1\right|=4\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-1=4\\2x-1=-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=5\\2x=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=-\dfrac{3}{2}\end{matrix}\right.\)

c) Ta có: \(\sqrt{\left(2x+1\right)^2}=3x-5\)

\(\Leftrightarrow\left|2x+1\right|=3x-5\)

\(\Leftrightarrow\left[{}\begin{matrix}2x+1=3x-5\left(x\ge-\dfrac{1}{2}\right)\\2x+1=5-3x\left(x< \dfrac{1}{2}\right)\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-3x=-5-1\\2x+3x=5-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=6\left(nhận\right)\\x=\dfrac{4}{5}\left(loại\right)\end{matrix}\right.\)

d) Ta có: \(\sqrt{4x-12}-14\sqrt{\dfrac{x-2}{49}}=\sqrt{9x-18}+8\)

\(\Leftrightarrow2\sqrt{x-3}-2\sqrt{x-2}=3\sqrt{x-2}+8\)

\(\Leftrightarrow2\sqrt{x-3}-5\sqrt{x-2}=8\)

\(\Leftrightarrow4\left(x-3\right)+25\left(x-2\right)-20\sqrt{x^2-5x+6}=8\)

\(\Leftrightarrow4x-12+25x-50-8=20\sqrt{\left(x-2\right)\left(x-3\right)}\)

\(\Leftrightarrow20\sqrt{\left(x-2\right)\left(x-3\right)}=29x-70\)

\(\Leftrightarrow x^2-5x+6=\dfrac{\left(29x-70\right)^2}{400}\)

\(\Leftrightarrow x^2-5x+6=\dfrac{841}{400}x^2-\dfrac{203}{20}x+\dfrac{49}{4}\)

\(\Leftrightarrow\dfrac{-441}{400}x^2+\dfrac{103}{20}x-\dfrac{25}{4}=0\)

\(\Delta=\left(\dfrac{103}{20}\right)^2-4\cdot\dfrac{-441}{400}\cdot\dfrac{-25}{4}=-\dfrac{26}{25}\)(Vô lý)

vậy: Phương trình vô nghiệm

1a.

ĐKXĐ: \(x\ne\left\{1;3\right\}\)

\(\Leftrightarrow\dfrac{6}{x-1}=\dfrac{4}{x-3}+\dfrac{4}{x-3}\)

\(\Leftrightarrow\dfrac{3}{x-1}=\dfrac{4}{x-3}\Leftrightarrow3\left(x-3\right)=4\left(x-1\right)\)

\(\Leftrightarrow3x-9=4x-4\Rightarrow x=-5\)

b.

ĐKXĐ: \(x\ne\left\{-1;2\right\}\)

\(\Leftrightarrow\dfrac{5}{x+1}=\dfrac{3}{2-x}+\dfrac{1}{2-x}\)

\(\Leftrightarrow\dfrac{5}{x+1}=\dfrac{4}{2-x}\Leftrightarrow5\left(2-x\right)=4\left(x+1\right)\)

\(\Leftrightarrow10-2x=4x+4\Leftrightarrow6x=6\Rightarrow x=1\)

1c.

ĐKXĐ: \(x\ne\left\{2;5\right\}\)

\(\Leftrightarrow\dfrac{3x\left(x-5\right)}{\left(x-2\right)\left(x-5\right)}-\dfrac{x\left(x-2\right)}{\left(x-2\right)\left(x-5\right)}=\dfrac{-3x}{\left(x-2\right)\left(x-5\right)}\)

\(\Leftrightarrow3x\left(x-5\right)-x\left(x-2\right)=-3x\)

\(\Leftrightarrow2x^2-10x=0\Leftrightarrow2x\left(x-5\right)=0\Rightarrow\left[{}\begin{matrix}x=0\\x=5\left(loại\right)\end{matrix}\right.\)

2a.

\(\Leftrightarrow-4x^2-5x+6=x^2+4x+4\)

\(\Leftrightarrow5x^2+9x-2=0\Rightarrow\left[{}\begin{matrix}x=-2\\x=\dfrac{1}{5}\end{matrix}\right.\)

2b.

\(2x^2-6x+1=0\Rightarrow x=\dfrac{3\pm\sqrt{7}}{2}\)