

08/07/2024
06/07/2024
$\displaystyle \begin{array}{{>{\displaystyle}l}}
17) \ ( 2x-1)( 5x-7) =( 2x-1)( 9-7x)\\
\Leftrightarrow ( 2x-1)( 5x-7-9+7x) =0\\
\Leftrightarrow ( 2x-1)( 12x-16) =0\\
\Leftrightarrow \left[ \begin{array}{l l}
2x-1=0 & \\
12x-16=0 &
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l l}
2x=1 & \\
12x=16 &
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l l}
x=\frac{1}{2} & \\
x=\frac{16}{12} =\frac{4}{3} &
\end{array} \right.\\
18) \ ( x-2)( 7-3x) =( 3x-7)( 8x+32)\\
\Leftrightarrow ( 3x-7)( 8x+32) +( x-2)( 3x-7) =0\\
\Leftrightarrow ( 3x-7)( 8x+32+x-2) =0\\
\Leftrightarrow ( 3x-7)( 9x+30) =0\\
\Leftrightarrow \left[ \begin{array}{l l}
3x-7=0 & \\
9x+30=0 &
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l l}
x=\frac{7}{3} & \\
x=\frac{-10}{3} &
\end{array} \right.\\
19) \ ( 2-x)( x+1) =( x-2)( 3x+5)\\
\Leftrightarrow ( x-2)( 3x+5) +( x-2)( x+1) =0\\
\Leftrightarrow ( x-2)( 3x+5+x+1) =0\\
\Leftrightarrow ( x-2)( 4x+6) =0\\
\Leftrightarrow \left[ \begin{array}{l l}
x-2=0 & \\
4x+6=0 &
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l l}
x=2 & \\
x=\frac{-3}{2} &
\end{array} \right.
\end{array}$
06/07/2024
17)
$\displaystyle ( 2x-1)( 5x-7) =( 2x-1)( 9-7x)$
$\displaystyle \Leftrightarrow ( 2x-1)( 5x-7) -( 2x-1)( 9-7x) =0$
$\displaystyle \Leftrightarrow ( 2x-1)( 5x-7-9+7x) =0$
$\displaystyle \Leftrightarrow ( 2x-1)( 12x-16) =0\Leftrightarrow \left[ \begin{array}{l l}
x=\frac{1}{2} & \\
x=\frac{4}{3} &
\end{array} \right.$
19) $\displaystyle ( 2-x)( x+1) =( x-2)( 3x+5)$
$\displaystyle \Leftrightarrow ( 2-x)( x+1) -( x-2)( 3x+5) =0$
$\displaystyle \Leftrightarrow ( 2-x)( x+1) +( 2-x)( 3x+5) =0$
$\displaystyle \Leftrightarrow ( 2-x)( x+1+3x+5) =0\Leftrightarrow ( 2-x)( 4x+6) =0$
$\displaystyle \Leftrightarrow \left[ \begin{array}{l l}
x=2 & \\
x=\frac{-3}{2} &
\end{array} \right.$
21) $\displaystyle ( 6x-7)( 3x+4) =( 7-6x)( x-1)$
$\displaystyle \Leftrightarrow ( 6x-7)( 3x+4) -( 7-6x)( x-1) =0$
$\displaystyle \Leftrightarrow ( 6x-7)( 3x+4) +( 6x-7)( x-1) =0$
$\displaystyle \Leftrightarrow ( 6x-7)( 3x+4+x-1) =0$
$\displaystyle \Leftrightarrow ( 6x-7)( 4x+3) =0\Leftrightarrow \left[ \begin{array}{l l}
x=\frac{7}{6} & \\
x=-\frac{3}{4} &
\end{array} \right.$
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