i,2.|x-3|+4=6 j,27-3.|2x-4|=3 k,|2x+4|= x – 4

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1. `i. 2. |x-3|+4=6`

   `=> 2. |x-3|=6-4`

   `=> 2. |x-3|=2`

   `=> |x-3|=2: 2`

   `=> |x-3|=1`

   `=> x-3=1` hoặc `x-3=-1`

   $+)$ `x-3=1`

   `x=1+3`

   `x=4`

   $+)$ `x-3=-1`

   `x=-1+3`

   `x=2`

   Vậy `x \in {2; 4}.`

   `j. 27-3. |2x-4|=3`

   `=> 3. |2x-4|=27-3`

   `=> 3. |2x-4|=24`

   `=> |2x-4|=24: 3`

   `=> |2x-4|=8`

   `=> 2x-4=8` hoặc `2x-4=-8`

   $+)$ `2x-4=8`

   `2x=8+4`

   `2x=12`

   `x=12: 2`

   `x=6`

   $+)$ `2x-4=-8`

   `2x=-8+4`

   `2x=-4`

   `x=-4: 2`

   `x=-2`

   Vậy `x \in {-2; 6}.`

   `k. |2x+4|= x – 4`

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

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

   \(\left[ \begin{array}{l}x=-8\\x=0\end{array} \right.\)

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2. i, 2 . | x – 3 | + 4 = 6

      2 . | x – 3 |       = 2

           | x – 3 |       = 1

   `=>` \(\left[ \begin{array}{l}x-3=1\\x-3=-1\end{array} \right.\) 

   `=>` \(\left[ \begin{array}{l}x=4\\x=2\end{array} \right.\) 

      Vậy x ∈ { 2 ; 4 }

   j, 27 – 3 . | 2x – 4 | = 3

             3 . | 2x – 4 | = 9

                  | 2x – 4 | = 3

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

   `=>` \(\left[ \begin{array}{l}2x=7\\2x=1\end{array} \right.\) 

   `=>` \(\left[ \begin{array}{l}x=\frac{7}{2}\\x=\frac{1}{2}\end{array} \right.\) 

      Vậy x ∈ { `7/2` ; `1/2` }

   k, | 2x + 4 | = x – 4 

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

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

   `=>` \(\left[ \begin{array}{l}x=-8\\x=0\end{array} \right.\) 

      Vậy x ∈ { -8 ; 0 } 

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