`a, |x - 2,5| - 3/4 = 0`
$\Leftrightarrow$ `|x - 2,5| = 0 + 3/4`
$\Leftrightarrow$ `|x - 5/2| = 3/4`
$\text{TH1:}$
`x - 5/2 = 3/4`
$\Leftrightarrow$ `x = 3/4 + 5/2`
$\Leftrightarrow$ `x = 13/4`
$\text{TH2:}$
`x - 5/2 = -3/4`
$\Leftrightarrow$ `x = -3/4 + 5/2`
$\Leftrightarrow$ `x = 7/4`
$\text{Vậy}$ `S = {13/4 ; 7/4}`
___________________
`b, 1/2 - |5/4 - 2x| = 1/3`
$\Leftrightarrow$ ` |5/4 - 2x| = 1/2 - 1/3`
$\Leftrightarrow$ ` |5/4 - 2x| = 1/6`
$\text{TH1:}$
`5/4 - 2x = 1/6`
$\Leftrightarrow$ `2x = 5/4 - 1/6`
$\Leftrightarrow$ `2x = 13/12`
$\Leftrightarrow$ `x = 13/12 : 2`
$\Leftrightarrow$ `x = 13/24`
$\text{TH2:}$
`5/4 - 2x = -1/6`
$\Leftrightarrow$ `2x = 5/4 + 1/6`
$\Leftrightarrow$ `2x = 17/12`
$\Leftrightarrow$ `x = 17/12 : 2`
$\Leftrightarrow$ `x = 17/24`
$\text{Vậy}$ `S = {13/24 ; 17/24}`
__________________
`c, |0,5x - 2| - |x + 2/3| = 0 (1)`
$\text{TH1:}$ `|0,5x - 2| - |x + 2/3| \ge 0`
$\Leftrightarrow$ `|0,5x - 2| = |x + 2/3|`
$\Leftrightarrow$ `(0,5x - 2) = (x + 2/3)`
$\Leftrightarrow$ `0,5x - 2 = x + 2/3`
$\Leftrightarrow$ `0,5x - x = 2 + 2/3`
$\Leftrightarrow$ `-0,5x = 8/3`
$\Leftrightarrow$ `-1/2x = 8/3`
$\Leftrightarrow$ `x = 8/3 : (-1}/2`
$\Leftrightarrow$ `x = -16/3`
$\text{Thay}$ `x = -16/3` $\text{vào (1) ta có:}$
`|0,5 . {-16}/3 - 2| - |{-16}/3 + 2/3|`
`= |{-8}/3 - 2| - |{-14}/3|`
`= |{-14}/3| - 14/3`
`= 14/3 - 14/3`
`= 0` $\text{(KTM)}$
$\text{TH2:}$ `|0,5x - 2| - |x + 2/3| < 0`
$\Leftrightarrow$ `|0,5x - 2| = -|x + 2/3|`
$\Leftrightarrow$ `(0,5x - 2) = -(x + 2/3)`
$\Leftrightarrow$ `0,5x - 2 = -x - 2/3`
$\Leftrightarrow$ `0,5x + x = 2 - 2/3`
$\Leftrightarrow$ `3/2x = 4/3`
$\Leftrightarrow$ `x = 4/3 : 3/2`
$\Leftrightarrow$ `x = 8/9`
$\text{Thay}$ `x = 8/9` $\text{vào (1) ta có:}$
`|0,5 . 8/9 - 2| - |8/9 + 2/3|`
`= |4/9 - 2| - |14/9|`
`= |-14/9| - |14/9|`
`= 14/9 - 14/9`
`= 0` $\text{(TM)}$
$\text{Vậy}$ `S = {-16/3 ; 8/9}`
_____________________
`d, 2x - |x + 1| = -1/2 (1)`
$\text{TH1:}$ `|x + 1| \ge 0`
$\Leftrightarrow$ `2x - (x + 1) = -1/2`
$\Leftrightarrow$ `2x - x - 1 = -1/2`
$\Leftrightarrow$ `x - 1 = -1/2`
$\Leftrightarrow$`x = -1/2 + 1`
$\Leftrightarrow$ `x = 1/2`
$\text{Thay}$ `x = 1/2` $\text{vào (1) ta có:}$
`2 . 1/2 - |1/2 + 1|`
`= 2 . 1/2 - |3/2|`
`= 1 - 3/2`
`= 1/2` $\text{(TM)}$
$\text{TH2:}$ `|x + 1| < 0`
`2x + (x + 1) = -1/2`
$\Leftrightarrow$ `2x + x + 1 = -1/2`
$\Leftrightarrow$ `3x + 1 = -1/2`
$\Leftrightarrow$ `3x = -1/2 - 1`
$\Leftrightarrow$ `3x = -3/2`
$\Leftrightarrow$ `x = -3/2 : 3`
$\Leftrightarrow$ `x = -1/2`
$\text{Thay}$ `x = -1/2` $\text{vào (1) ta có:}$
`2 . {-1}/2 - |-1/2 + 1|`
`= -1 - |1/2|`
`= -1 - 1/2`
`= -3/2` $\text{(KTM)}$
$\text{Vậy}$ `S = {1/2}`
