1: \(x-2=2x-4\left(x-1\right)\)
=>2x-4x+4=x-2
=>-2x+4-x+2=0
=>-3x+6=0
=>-3x=-6
=>x=2
2: \(\dfrac{1-2x}{3}=\dfrac{4x-5}{6}\)
=>\(\dfrac{2\left(1-2x\right)}{6}=\dfrac{4x-5}{6}\)
=>2-4x=4x-5
=>-8x=-7
=>\(x=\dfrac{7}{8}\)
3: \(\left(x+2\right)^2-x\left(x+2\right)=0\)
=>(x+2)(x+2-x)=0
=>2(x+2)=0
=>x+2=0
=>x=-2
4: \(\dfrac{2x+9}{65}+\dfrac{2x+11}{63}=\dfrac{2x+13}{61}+\dfrac{2x+15}{59}\)
=>\(\left(\dfrac{2x+9}{65}+1\right)+\left(\dfrac{2x+11}{63}+1\right)=\left(\dfrac{2x+13}{61}+1\right)+\left(\dfrac{2x+15}{59}+1\right)\)
=>\(\dfrac{2x+74}{65}+\dfrac{2x+74}{63}-\dfrac{2x+74}{61}-\dfrac{2x+74}{59}=0\)
=>2x+74=0
=>2x=-74
=>x=-37
1) \(x-2=2x-4\left(x-1\right)\)
\(\Leftrightarrow x-2=2x-4x+4\)
\(\Leftrightarrow x-2=-2x+4\)
\(\Leftrightarrow3x=6\)
\(\Leftrightarrow x=2\)
2) \(\dfrac{1-2x}{3}=\dfrac{4x-5}{6}\)
\(\Leftrightarrow2\left(1-2x\right)=4x-5\)
\(\Leftrightarrow2-4x=4x-5\)
\(\Leftrightarrow8x=7\)
\(\Leftrightarrow x=\dfrac{7}{8}\)
3) \(\left(x+2\right)^2-x\left(x+2\right)=0\)
\(\Leftrightarrow2\left(x+2\right)=0\)
\(\Leftrightarrow x=-2\)
4) \(\dfrac{2x+9}{65}+\dfrac{2x+11}{63}=\dfrac{2x+13}{61}+\dfrac{2x+15}{59}\)
\(\Leftrightarrow\left(\dfrac{2x+9}{65}+1\right)+\left(\dfrac{2x+11}{63}+1\right)=\left(\dfrac{2x+13}{61}+1\right)+\left(\dfrac{2x+15}{59}+1\right)\)
\(\Leftrightarrow\dfrac{2x+74}{65}+\dfrac{2x+74}{63}-\dfrac{2x+74}{61}-\dfrac{2x+74}{59}=0\)
\(\Leftrightarrow\left(2x+74\right)\left(\dfrac{1}{65}+\dfrac{1}{63}-\dfrac{1}{61}-\dfrac{1}{59}\right)=0\)
\(\Leftrightarrow2x+74=0\)
\(\Leftrightarrow x=-37\)
