Đáp án:

 `||1/2 x + 2/3| + 3/4| = 4/5`

Vì `| 1/2 x + 2/3| ≥ 0`

Nên `||1/2 x + 2/3| + 3/4| = 4/5`

`⇔ |1/2 x + 2/3 + 3/4| = 4/5`

`⇔ |1/2 x + 17/12| = 4/5`

`⇒` $\left[\begin{matrix} \dfrac{1}{2}x + \dfrac{17}{12} = \dfrac{4}{5}\\ \dfrac{1}{2}x + \dfrac{17}{12} = \dfrac{-4}{5}\end{matrix}\right.$

`⇒` $\left[\begin{matrix} \dfrac{1}{2}x  = \dfrac{4}{5} - \dfrac{17}{12}\\ \dfrac{1}{2}x = \dfrac{-4}{5}- \dfrac{17}{12} \end{matrix}\right.$

`⇒` $\left[\begin{matrix} \dfrac{1}{2}x = \dfrac{-37}{60}\\ \dfrac{1}{2}x = \dfrac{-133}{60}\end{matrix}\right.$

`⇒` $\left[\begin{matrix}x = \dfrac{-37}{60} : \dfrac{1}{2} \\ x = \dfrac{-133}{60} : \dfrac{1}{2}\end{matrix}\right.$

`⇒` $\left[\begin{matrix}x = \dfrac{-37}{30}\\ x = \dfrac{-133}{30}\end{matrix}\right.$

Vậy `x = -37/30` hoặc `x = -133/30`

Đáp án:

`x=(-37)/(30); x=(-17)/(15)`

Giải thích các bước giải:

`||(1)/(2)x+(2)/(3)|+(3)/(4)|=(4)/(5)`

`⇒|(1)/(2)x+(2)/(3)|+(3)/(4)=(4)/(5)`

`   |(1)/(2)x+(2)/(3)|            =(4)/(5)-(3)/(4)`

`   |(1)/(2)x+(2)/(3)|            =(16-15)/(20)`

`   |(1)/(2)x+(2)/(3)|            =(1)/(20)`

`⇒`\(\left[ \begin{array}{l}\dfrac{1}{2}x+\dfrac{2}{3}=\dfrac{1}{20}\\\dfrac{1}{2}x+\dfrac{2}{3}=-\dfrac{1}{20}\end{array} \right.\) 

`⇒`\(\left[ \begin{array}{l}\dfrac{1}{2}x=\dfrac{1}{20}-\dfrac{2}{3}\\\dfrac{1}{2}x=-\dfrac{1}{20}-\dfrac{2}{3}\end{array} \right.\) 
`⇒`\(\left[ \begin{array}{l}x=\dfrac{3-40}{60}:\dfrac{1}{2}\\x=-\dfrac{3+40}{60}:\dfrac{1}{2}\end{array} \right.\)

`⇒`\(\left[ \begin{array}{l}x=\dfrac{-37}{60}.2\\x=-\dfrac{34}{60}.2\end{array} \right.\) 
`⇒`\(\left[ \begin{array}{l}x=\dfrac{-37}{30}\\x=\dfrac{-34}{30}\end{array} \right.\)

`⇒`\(\left[ \begin{array}{l}x=\dfrac{-37}{30}\\x=\dfrac{-17}{15}\end{array} \right.\) 

Vậy `x=(-37)/(30); x=(-17)/(15)`

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