Đáp án:

`a) x =` `(-7)/2`

`b) x =` `4/5` 

`c) x ∈ {` `33/80` ; `(-17)/80` `}`

`d) x ∈ {` `3/8` ; `5/8` `}`

Giải thích các bước giải:

`a)` `3/2` `+ 2x = -` 5`1/2`

`=>` `3/2` `+ 2x =` `(-11)/2` 

`=> 2x =` `(-11)/2` `-` `3/2`

`=> 2x =` `(-14)/2`

`=> 2x = - 7`

`=> x =` `(-7)/2`

Vậy `x =` `(-7)/2`

`b)` `3/5` `-` `1/4` `. x =` `2/5`

`=>`  `1/4` `. x =` `3/5` `-` `2/5`

`=>`  `1/4` `. x =` `1/5`

`=> x =` `1/5` `:` `1/4`

`=> x =` `1/5` . 4

`=> x =` `4/5`

Vậy `x =` `4/5`

`c) | 2x -` `1/5` `| -` `1/4` `=` `3/8`

`=> | 2x -` `1/5` `| =` `3/8` `+` `1/4`

`=> | 2x -` `1/5` `| =` `3/8` `+` `2/8`

`=> |` 2x - `1/5` `| =` `5/8`

`=> 2x -` `1/5` `∈ {` `5/8` ; `(-5)/8` `}`

Trường hợp `1 :`

`2x -` `1/5` `=` `5/8`

`=> 2x =` `5/8` `+` `1/5`

`=> 2x =` `25/40` `+` `8/40`

`=> 2x =` `33/40` 

`=> x =` `33/40` `: 2`

`=> x =` `33/40` . `1/2`

`=> x =` `33/80`

Trường hợp `2 :`

`2x -` `1/5` `=` `(-5)/8`

`=> 2x =`  `(-5)/8` `+` `1/5`

`=> 2x =`  `(-25)/40` `+` `8/40`

`=> 2x =` `(-17)/40`

`=> x =`  `(-17)/40` . `1/2`

`=> x =` `(-17)/80`

Vậy `x ∈ {` `33/80` ; `(-17)/80`` }`

`d)` `1/2` `- | 2x - 1 | =` `1/4`

`=> | 2x - 1 | =` `2/4` `-` `1/4`

`=> | 2x - 1 | =` `1/4`

`=> 2x - 1 ∈ {` `1/4` ; `(-1)/4` `}`

Trường hợp `1 :`

`2x - 1 =` `1/4`

`=> 2x =` `1/4` `+ 1`

`=> 2x =` `5/4`

`=> x =` `5/4` . `1/2`

`=> x =` `5/8`

Trường hợp `2 :`

`2x - 1 =` `(-1)/4`

`=> 2x `=` ``(-1)/4` `+ 1`

`=> 2x =` `3/4`

`=> x =` `3/4` . `1/2`

`=> x =` `3/8`

Vậy `x ∈ {`  `3/8` ; `5/8` `}`