Bài 1.3 : Tìm x, biết : a, 2|3x – 1|+ 1= 5 b, |x/2 – 1| = 3 c, |-x + 2/5| + 1/2 = 3,5 d, |x – 1/3| = 2/1/5

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1. Đáp án:

    `a) x=1` hoặc `x=-1/3`

   `b) x=8` hoặc `x=-4`

   `c) x=-13/5` hoặc `x=17/5`

   `d) x=38/15` hoặc `x=-28/15`

   Giải thích các bước giải:

   `a) 2|3x-1|+1=5`

   `⇔2|3x-1|=4`

   `⇔|3x-1|=2`

   `⇔`\(\left[ \begin{array}{l}3x-1=2\\3x-1=-2\end{array} \right.\) 

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

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

   vậy `x=1` hoặc `x=-1/3`

   `b) |x/2-1|=3`

   `⇔`\(\left[ \begin{array}{l}x/2-1=3\\x/2-1=-3\end{array} \right.\) 

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

   `⇔`\(\left[ \begin{array}{l}x=8\\x=-4\end{array} \right.\) 

   vậy `x=8` hoặc `x=-4`

   `c) |2/5-x|+1/2=3,5`

   `⇔|2/5-x|=7/2-1/2`

   `⇔|2/5-x|=3`

   `⇔`\(\left[ \begin{array}{l}2/5-x=3\\2/5-x=-3\end{array} \right.\) 

   `⇔`\(\left[ \begin{array}{l}x=2/5-3\\x=2/5+3\end{array} \right.\) 

   `⇔`\(\left[ \begin{array}{l}x=-13/5\\x=17/5\end{array} \right.\) 

   vậy `x=-13/5` hoặc `x=17/5`

   `d) |x-1/3|=2“1/5`

   `⇔|x-1/3|=11/5`

   `⇔`\(\left[ \begin{array}{l}x-1/3=11/5\\x-1/3=-11/5\end{array} \right.\) 

   `⇔`\(\left[ \begin{array}{l}x=11/5+1/3\\x=-11/5+1/3\end{array} \right.\) 

   `⇔`\(\left[ \begin{array}{l}x=38/15\\x=-28/15\end{array} \right.\) 

   vậy `x=38/15` hoặc `x=-28/15`

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