a) Ta có: \(3x-\dfrac{1}{2}+5\left(x-2\right)=\dfrac{2}{3}\left(x+1\right)\)
\(\Leftrightarrow3x-\dfrac{1}{2}+5x-10=\dfrac{2}{3}x+\dfrac{2}{3}\)
\(\Leftrightarrow8x-\dfrac{21}{2}-\dfrac{2}{3}x-\dfrac{2}{3}=0\)
\(\Leftrightarrow\dfrac{22}{3}x-\dfrac{67}{6}=0\)\(\Leftrightarrow x\cdot\dfrac{22}{3}=\dfrac{67}{6}\)
\(\Leftrightarrow x=\dfrac{67}{6}:\dfrac{22}{3}=\dfrac{67}{6}\cdot\dfrac{3}{22}=\dfrac{67}{44}\)
Vậy: \(S=\left\{\dfrac{67}{44}\right\}\)
b) Ta có: \(\left(2x-3\right)^2=\left(2x-3\right)\left(x+1\right)\)
\(\Leftrightarrow\left(2x-3\right)^2-\left(2x-3\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left(2x-3\right)\left(2x-3-x-1\right)=0\)
\(\Leftrightarrow\left(2x-3\right)\left(x-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-3=0\\x-4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=3\\x=4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=4\end{matrix}\right.\)
Vậy: \(S=\left\{\dfrac{3}{2};4\right\}\)
c) Ta có: \(2\left(x-3\right)+1=2\left(x+1\right)-9\)
\(\Leftrightarrow2x-6+1=2x+2-9\)
\(\Leftrightarrow-5=-7\)(Vô lý)
Vậy: \(S=\varnothing\)
d) Ta có: \(\dfrac{7x}{8}-5\left(x-9\right)=\dfrac{20x+1.5}{6}\)
\(\Leftrightarrow\dfrac{21x}{24}-\dfrac{120\left(x-9\right)}{24}=\dfrac{4\left(20x+1.5\right)}{24}\)
\(\Leftrightarrow21x-120x+1080=80x+6\)
\(\Leftrightarrow-99x+1080-80x-6=0\)
\(\Leftrightarrow-179x+1074=0\)
\(\Leftrightarrow-179x=-1074\)
hay x=6
Vậy: S={6}
f) Ta có: \(3\left(x+4\right)-5\left(x-2\right)=4\left(3x-1\right)+82\)
\(\Leftrightarrow3x+12-5x+10=12x-4+82\)
\(\Leftrightarrow-2x+22-12x-78=0\)
\(\Leftrightarrow-14x-56=0\)
\(\Leftrightarrow-14x=56\)
hay x=-4
Vậy: S={-4}
g) Ta có: \(\dfrac{x+17}{5}-\dfrac{3x-7}{4}=-2\)
\(\Leftrightarrow\dfrac{4\left(x+17\right)}{20}-\dfrac{5\left(3x-7\right)}{20}=\dfrac{-40}{20}\)
\(\Leftrightarrow4x+68-15x+35+40=0\)
\(\Leftrightarrow-11x+143=0\)
\(\Leftrightarrow-11x=-143\)
hay x=13
Vậy: S={13}
a) \(3x-\dfrac{1}{2}+5\left(x-2\right)=\dfrac{2}{3}\left(x+1\right)\)
\(\Leftrightarrow3x-\dfrac{1}{2}+5x-10=\dfrac{2}{3}x+\dfrac{2}{3}\)
\(\Leftrightarrow3x+5x-\dfrac{2}{3}x=\dfrac{1}{2}+10+\dfrac{2}{3}\)
\(\Leftrightarrow\left(3+5-\dfrac{2}{3}\right)x=\dfrac{67}{6}\)
\(\Leftrightarrow\dfrac{22}{3}x=\dfrac{67}{6}\)
\(\Leftrightarrow x=\dfrac{67}{44}\)
b) \(\left(2x-3\right)^2=\left(2x-3\right)\left(x+1\right)\)
\(\Leftrightarrow\left(2x-3\right)^2-\left(2x-3\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left(2x-3\right)\left(2x-3-x-1\right)=0\)
\(\Leftrightarrow\left(2x-3\right)\left(x-4\right)=0\)
\(\left[{}\begin{matrix}2x-3=0\\x-4=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=4\end{matrix}\right.\)
c) \(2\left(x-3\right)+1=2\left(x+1\right)-9\)
\(\Leftrightarrow2x-6+1=2x+2-9\)
\(\Leftrightarrow2x-5=2x-7\)
=> x vô nghiệm
d và e giống nhau) \(\dfrac{7x}{8}-5\left(x-9\right)=\dfrac{20x+1,5}{6}\)
\(\Leftrightarrow\dfrac{7x}{8}-5x+45=\dfrac{20x+1,5}{6}\)
\(\Leftrightarrow\dfrac{7x}{8}-\dfrac{40x}{8}+\dfrac{360}{8}=\dfrac{20x+1,5}{6}\)
\(\Leftrightarrow\dfrac{-33x+360}{8}=\dfrac{20x+1,5}{6}\)
\(\Leftrightarrow\dfrac{-99x+1080}{24}=\dfrac{80x+6}{24}\)
\(\Leftrightarrow-99x+1080=80x+6\)
\(\Leftrightarrow-179x=-1074\)
\(\Leftrightarrow x=6\)
f) \(3\left(x+4\right)-5\left(x-2\right)=4\left(3x-1\right)+82\)
\(\Leftrightarrow3x+12-5x+10=12x-4+82\)
\(\Leftrightarrow-2x+22=12x+78\)
\(\Leftrightarrow-14x=56\)
\(\Leftrightarrow x=-4\)
g) \(\dfrac{x+17}{5}-\dfrac{3x-7}{4}=-2\)
\(\Leftrightarrow\dfrac{x+17}{5}-\dfrac{3x-7}{4}+2=0\)
\(\Leftrightarrow\dfrac{4x+68-15x+35+40}{20}=\dfrac{0}{20}\)
\(\Leftrightarrow4x+68-15x+35+40=0\)
\(\Leftrightarrow-11x+143=0\)
\(\Leftrightarrow-11x=143\)
\(\Leftrightarrow x=-13\)
