Đáp án + Giải thích các bước giải:

 Bài `2`:

a, `0,5 - x = 3/2`

` 1/2 - x = 3/2`

` x = 1/2 - 3/2`

` x = -1`

Vậy `x = -1`

 b, `3/4 + 1/4 : x = 2/5`

` 1/4 : x = 2/5 - 3/4`

` 1/4 : x = 8/20 - 15/20`

` 1/4 : x = -7/20`

` x         = 1/4 : (-7)/20`

` x         = -5/7`

Vậy `x = -5/7`

c, `|1/3 x - 3/4| = 3/5`

`=> 1/3 x - 3/4 = 3/5 ` hoặc `1/3 x - 3/4 = -3/5`

Nếu `1/3 x - 3/4 = 3/5`           ;        Nếu `1/3 x - 3/4 = -3/5`

` 1/3 x = 3/5 + 3/4`               ;               `1/3 x = -3/5 + 3/4`

` 1/3 x = 12/20 + 15/20`      ;              `1/3 x = -12/20 + 15/20`

` 1/3 x = 27/20`                      ;             `1/3 x = 3/20`

` x       = 27/20 : 1/3`           ;              ` x = 3/20 : 1/3`

` x       = 81/20`                    ;         `x = 9/20`

Vậy `x \in {81/20 ; 9/20}`

d, `(2019 + 1/16x^4)^2 = 2020^2020 : 2020^2018`

` (2019 + 1/16x^4)^2 = 2020^2 = (-2020)^2`

`=> 2019 + 1/16x^4 = 2020` hoặc `2019 + 1/16 x^4 = -2020`

Vì `x^4 \ge 0 => 1/16 x^4 \ge 0` với mọi x

`=> 2019 + 1/16 x^4 \ge 2019`  với mọi x

 `=> 2019 + 1/16x^4 = 2020`   

`=> 1/16x^4 = 1`         

`=> x^4 = 16`

`=> x = \pm 2`

Vậy `x \in {2 ; -2}`

`a, 0,5 - x = 3/2`

$\Leftrightarrow$ `1/2 - x = 3/2`

$\Leftrightarrow$ `x = 1/2 - 3/2`

$\Leftrightarrow$ `x = -2/2`

$\Leftrightarrow$ `x = -1`

$\text{Vậy}$ `x = -1`

_______________

`b, 3/4 + 1/4 : x = 2/5`

$\Leftrightarrow$ `1/4 : x = 2/5 - 3/4`

$\Leftrightarrow$ `1/4 : x = -7/20`

$\Leftrightarrow$ `x = 1/4 : -7/20`

$\Leftrightarrow$ `x = -5/7`

$\text{Vậy}$ `x = -5/7`
___________________

`c, |1/3x - 3/4| = 3/5`

$\text{TH1:}$

`1/3x - 3/4 = 3/5`

$\Leftrightarrow$ `1/3x = 3/5 + 3/4`

$\Leftrightarrow$ `1/3x = 27/20`

$\Leftrightarrow$ `x = 27/20 : 1/3`

$\Leftrightarrow$ `x = 81/20`

$\text{TH2:}$

`1/3x - 3/4 = -3/5`

$\Leftrightarrow$ `1/3x = -3/5 + 3/4`

$\Leftrightarrow$ `1/3x = 3/20`

$\Leftrightarrow$ `x = 3/20 : 1/3`

$\Leftrightarrow$ `x = 9/20`

$\text{Vậy}$ `x \in {81/20 ; 9/20}`

_________________

`d, (2019 + 1/16 . x^{4})^{2} = 2020^{2020} : 2020 ^{2018}`

$\Leftrightarrow$ `(2019 + 1/16 . x^{4})^{2} = 2020^{2}`

$\Leftrightarrow$ `2019 + 1/16 . x^{4} = (+-2020)`

$\text{TH1:}$

`2019 + 1/16 . x^{4} = 2020`

$\Leftrightarrow$ `1/16 . x^{4} = 2020 - 2019`

$\Leftrightarrow$ `1/16 . x^{4} = 1`

$\Leftrightarrow$ `x^{4} = 1 : 1/16`

$\Leftrightarrow$ `x^{4} = 16`

$\Leftrightarrow$ `x^{4} = (+-2)^{4}`

$\Leftrightarrow$ `x = +-2`

$\text{TH2:}$

`2019 + 1/16 . x^{4} = -2020`

$\Leftrightarrow$ `1/16 . x^{4} = -2020 - 2019`

$\Leftrightarrow$ `1/16 . x^{4} = -4039`

$\Leftrightarrow$ `x^{4} = -4039 : 1/16`

$\Leftrightarrow$ `x^{4} = -64624`

$\text{Vì}$ `x^{4} \ge 0 `

`=>` $\text{Vô lí}$

$\text{Vậy}$ `x \in {2 ; -2}`