a) \(4\left(3-2x\right)=\left(x-6\right)+5\)
\(\Leftrightarrow12-8x=x-6+5\)
\(\Leftrightarrow12-8x=x-1\)
\(\Leftrightarrow x+8x=12+1\)
\(\Leftrightarrow9x=13\)
\(\Leftrightarrow x=\dfrac{13}{9}\)
b) \(8x^2+x-300=4x\left(2x-25\right)+3\)
\(\Leftrightarrow8x^2+x-300=8x^2-100x+3\)
\(\Leftrightarrow8x^2-8x^2+x+100x-300-3=0\)
\(\Leftrightarrow101x-303=0\)
\(\Leftrightarrow101x=303\)
\(\Leftrightarrow x=3\)
c) \(2x+\dfrac{3x+1}{6}=\dfrac{3x+2}{2}-\dfrac{5}{3}\)
\(\Leftrightarrow\dfrac{12x}{6}+\dfrac{3x+1}{6}=\dfrac{3\left(3x+2\right)}{6}-\dfrac{2\cdot5}{6}\)
\(\Leftrightarrow12x+3x+1=9x+6-10\)
\(\Leftrightarrow15x-9x=6-10-1\)
\(\Leftrightarrow6x=-5\)
\(\Leftrightarrow x=-\dfrac{5}{6}\)
d) \(x+\dfrac{x+8}{6}-7=\dfrac{2x-2}{5}+\dfrac{x-1}{3}\)
\(\Leftrightarrow\dfrac{30x}{30}+\dfrac{5\left(x+8\right)}{30}-\dfrac{7\cdot30}{30}=\dfrac{6\left(2x-2\right)}{30}+\dfrac{10\left(x-1\right)}{30}\)
\(\Leftrightarrow30x+5x+40-210=12x-12+10x-10\)
\(\Leftrightarrow35x-170=22x-22\)
\(\Leftrightarrow13x=148\)
\(\Leftrightarrow x=148:13\)
\(\Leftrightarrow x=\dfrac{148}{13}\)
e) \(\dfrac{2\left(x-3\right)}{7}-x+2=\dfrac{13x+4}{21}\)
\(\Leftrightarrow\dfrac{3\cdot2\left(x-3\right)}{21}-\dfrac{21\cdot\left(x-2\right)}{21}=\dfrac{13+4x}{21}\)
\(\Leftrightarrow6\left(x-3\right)-21\left(x-2\right)=13x+4\)
\(\Leftrightarrow6x-18-21x+42=13x+4\)
\(\Leftrightarrow-15x+24=13x+4\)
\(\Leftrightarrow13x+15x=24-4\)
\(\Leftrightarrow28x=20\)
\(\Leftrightarrow x=\dfrac{5}{7}\)
f) \(\dfrac{4x+2}{5}+\dfrac{8x-1}{3}=\dfrac{5x+2}{6}+5\)
\(\Leftrightarrow\dfrac{6\left(4x+2\right)}{30}+\dfrac{10\left(8x-1\right)}{30}=\dfrac{5\left(5x+2\right)}{30}+\dfrac{5\cdot30}{30}\)
\(\Leftrightarrow24x+12+80x-10=25x+10+150\)
\(\Leftrightarrow104x+2=25x+160\)
\(\Leftrightarrow104x-25x=160-2\)
\(\Leftrightarrow79x=158\)
\(\Leftrightarrow x=2\)
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