Bài 1:giải các phương trình sau: a)|3x|=x+7 b)|-4x|=-2x+11 c)|x-9|=2x+5 d)|3x|-1=4x+1 e)|3x|-x-4

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1. a)

   `|3x|=x+7`

   ⇔\(\left[ \begin{array}{l}3x=x+7\\-3x=x+7\end{array} \right.\) 

   ⇔\(\left[ \begin{array}{l}2x=7\\x=-4x=7\end{array} \right.\)  

   ⇔\(\left[ \begin{array}{l}x=\frac{7}{2}\\x=\frac{-4}{7}\end{array} \right.\)

   b)

   `|-4x|=-2x+11`

   ⇔\(\left[ \begin{array}{l}4x=-2x+11\\-4x=-2x+11\end{array} \right.\) 

   ⇔\(\left[ \begin{array}{l}6x=11\\-2x=11\end{array} \right.\) 

   ⇔\(\left[ \begin{array}{l}x=\frac{11}{6}\\x=\frac{-11}{2}\end{array} \right.\)  

   c)

   `|x-9|=2x+5`

   ⇔\(\left[ \begin{array}{l}x-9=2x+5\\9-x=2x+5\end{array} \right.\) 

   ⇔\(\left[ \begin{array}{l}x=-14\\-3x=-4\end{array} \right.\) 

   ⇔\(\left[ \begin{array}{l}x=-14\\x=\frac{4}{3}\end{array} \right.\)  

   d)

   `|3x|-1=4x+1`

   ⇔`|3x|=4x+2`

   ⇔\(\left[ \begin{array}{l}3x=4x+2\\-3x=4x+2\end{array} \right.\) 

   ⇔\(\left[ \begin{array}{l}x=-2\\7x=-2\end{array} \right.\) 

   ⇔\(\left[ \begin{array}{l}x=-2\\x=\frac{-2}{7}\end{array} \right.\) 

   e)

   `|3x|-x-4 `

   ⇔\(\left[ \begin{array}{l}3x-x-4\\-3x-x-4\end{array} \right.\) 

   ⇔\(\left[ \begin{array}{l}2x-4\\-4x-4\end{array} \right.\) 

    

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