Giải phương trình sau: 15/4- 2,5 : |3/4x + 1/2| = 3

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1. ` 15/4- 2,5 : |3/4x + 1/2| = 3`

   `⇔2,5 : |3/4x + 1/2|=3/4`

   `⇔ |3/4x + 1/2|=(10)/3`

   `⇔`\(\left[ \begin{array}{l}3/4x + 1/2=(-10)/3\\3/4x + 1/2=(10)/3\end{array} \right.\) 

   `⇔`\(\left[ \begin{array}{l}3/4x =(-23)/6\\3/4x=(17)/6\end{array} \right.\) 

   `⇔`\(\left[ \begin{array}{l}x =(-46)/6\\x=(34)/9\end{array} \right.\) 

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2. Đáp án:

    `S={(34)/9;(-46)/9}`

   Giải thích các bước giải:

    `(15)/4 – 2,5 : |3/4x+1/2|=3`

   `⇔25/10 : |3/4x+1/2|=(15)/4 – 3`

   `⇔5/2 : |3/4x+1/2|=3/4`

   `⇔|3/4x+1/2|=5/2 : 3/4`

   `⇔|3/4x+1/2|=(10)/3`

   `⇔`\(\left[ \begin{array}{l}\dfrac{3}{4}x+\dfrac{1}{2}=\dfrac{10}{3}\\\dfrac{3}{4}x+\dfrac{1}{2}=\dfrac{-10}{3}\end{array} \right.\) 

   `⇔`\(\left[ \begin{array}{l}\dfrac{3}{4}x=\dfrac{10}{3}-\dfrac{1}{2}\\\dfrac{3}{4}x=\dfrac{-10}{3}-\dfrac{1}{2}\end{array} \right.\) 

   `⇔`\(\left[ \begin{array}{l}\dfrac{3}{4}x=\dfrac{17}{6}\\\dfrac{3}{4}x=\dfrac{-23}{6}\end{array} \right.\) 

   `⇔`\(\left[ \begin{array}{l}x=\dfrac{34}{9}\\x=\dfrac{-46}{9}\end{array} \right.\) 

   Vậy `S={(34)/9;(-46)/9}`

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