Bài `10:`

`a)`

`|x - 2| = 2`

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

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

`=>` \(\left[ \begin{array}{l}x = 4\\x = 0\end{array} \right.\)

`Vậy: x ∈ {4; 0}`

`b)`

`|x + 1| = 2`

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

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

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

`Vậy: x ∈ {1; -3}`

Bài `11:`

`a)`

`|x - 4/5| = 3/4`

`=>` $\left[\begin{matrix} x - \dfrac{4}{5} = \dfrac{3}{4}\\ x - \dfrac{4}{5} = \dfrac{-3}{4}\end{matrix}\right.$

`=>` $\left[\begin{matrix} x = \dfrac{3}{4} + \dfrac{4}{5}\\ x = \dfrac{-3}{4} + \dfrac{4}{5}\end{matrix}\right.$

`=>` $\left[\begin{matrix} x = \dfrac{31}{20}\\  = \dfrac{1}{20}\end{matrix}\right.$

`Vậy: x ∈ {31/20; 1/20}`

`b)`

`6 - |1/2 - x| = 2/5`

`|1/2 - x| = 6 - 2/5`

`|1/2 - x| = 28/5`

`=>` $\left[\begin{matrix} \dfrac{1}{2} - x = \dfrac{28}{5}\\ \dfrac{1}{2} - x = \dfrac{-28}{5}\end{matrix}\right.$

`=>` $\left[\begin{matrix} x = \dfrac{1}{2} - \dfrac{28}{5}\\ x = \dfrac{1}{2} - \dfrac{-28}{5}\end{matrix}\right.$

`=>` $\left[\begin{matrix} x = \dfrac{-51}{10}\\ x = \dfrac{61}{10}\end{matrix}\right.$

`Vậy: x ∈ {-51/20; 61/10}`

`c)`

`|x + 3/5| - 1/2 = 1/2`

`|x + 3/5| = 1/2 + 1/2`

`|x + 3/5| = 1`

`=>` $\left[\begin{matrix} x + \dfrac{3}{5} = 1\\ x + \dfrac{3}{5} = 1\end{matrix}\right.$

`=>` $\left[\begin{matrix} x = 1 - \dfrac{3}{5}\\ x = -1 - \dfrac{3}{5}\end{matrix}\right.$

`=>` $\left[\begin{matrix} x = \dfrac{2}{5}\\ x = \dfrac{-3}{5}\end{matrix}\right.$

`Vậy: x ∈ {2/5; -3/5}`

`d)`

`2 - |x - 2/5| = -1/2`

`|x - 2/5| = 2 - (-1/2)`

`|x - 2/5| = 5/2`

`=>` $\left[\begin{matrix} x - \dfrac{2}{5} + \dfrac{5}{2} \\ x - \dfrac{2}{5} +\dfrac{-5}{2}\end{matrix}\right.$

`=>` $\left[\begin{matrix} x = \dfrac{5}{2} + \dfrac{2}{5}\\ \dfrac{-5}{2} + \dfrac{2}{5}\end{matrix}\right.$

`=>` $\left[\begin{matrix} x = \dfrac{29}{10}\\ x = \dfrac{-21}{10}\end{matrix}\right.$

`Vậy: x ∈ {29/10; -21/10}`

`e)`

`0,2 + |x - 2,3| = 1,1`

`|x - 2,3| = 1,1 - 0,2`

`|x - 2,3| = 0,9`

`=>` \(\left[ \begin{array}{l}x - 2,3 = 0,9\\x - 2,3 = -0,9\end{array} \right.\)

`=>` \(\left[ \begin{array}{l}x = 0,9 + 2,3\\x = -0,9 + 2,3\end{array} \right.\)

`=>` \(\left[ \begin{array}{l}x = 3,3\\x = 1,4\end{array} \right.\) 

`Vậy: x ∈ {3,3; 1,4}`

`f)`

`-1 + |x + 4,5| = (-6,2)`

`|x + 4,5| = (-6,2) - (-1)`

`|x + 4,5| = (-5,2)`

`Vì: (-5,2) < 0`

`=>` Ta chỉ có `1` trường hợp

`x + 4,5 = (-5,2)`

`x = (-5,2) - 4,5`

`x = (-9,7)`

`Vậy: x ∈ {-9,7}`