Toán Lớp 6: Tìm x
a) 2x+6 chia hết cho 2x-1
b) 3x+7 chia hết cho 3x-1
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Toán Lớp 6: Tìm x
a) 2x+6 chia hết cho 2x-1
b) 3x+7 chia hết cho 3x-1
Comments ( 1 )
a)2x + 6 = 2x – 1 + 7\\
Do:\left( {2x – 1} \right) \vdots \left( {2x – 1} \right)\\
Khi:2x + 6 \vdots \left( {2x – 1} \right)\\
\Leftrightarrow 7 \vdots \left( {2x – 1} \right)\\
\Leftrightarrow \left( {2x – 1} \right) \in U\left( 7 \right)\\
\Leftrightarrow 2x – 1 \in \left\{ { – 7; – 1;1;7} \right\}\\
\Leftrightarrow 2x \in \left\{ { – 6;0;2;8} \right\}\\
\Leftrightarrow x \in \left\{ { – 3;0;1;4} \right\}\\
Vậy\,x \in \left\{ { – 3;0;1;4} \right\}\\
b)3x + 7 = 3x – 1 + 8\\
Do:\left( {3x – 1} \right) \vdots \left( {3x – 1} \right)\\
\Leftrightarrow 8 \vdots \left( {3x – 1} \right)\\
\Leftrightarrow \left( {3x – 1} \right) \in U\left( 8 \right)\\
\Leftrightarrow 3x – 1 \in \left\{ { – 8; – 4; – 2; – 1;1;2;4;8} \right\}\\
\Leftrightarrow 3x \in \left\{ { – 7; – 3; – 1;0;2;3;5;9} \right\}\\
\Leftrightarrow x \in \left\{ { – \dfrac{7}{3}; – 1; – \dfrac{1}{3};0;\dfrac{2}{3};1;\dfrac{5}{3};3} \right\}\\
Do:x \in Z\\
\Leftrightarrow x \in \left\{ { – 1;0;1;3} \right\}\\
Vậy\,x \in \left\{ { – 1;0;1;3} \right\}
\end{array}$