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

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}`