Đáp án + giải thích các bước giải:

`a)` `(7/2+2x):3/14=7/12`

`7/2+2x=7/12*3/14`

`7/2+2x=1/8`

`2x=1/8-7/2`

`2x=-27/8`

`x=-27/8:2`

`x=-27/16`

Vậy `x=-27/16`.

`b)` `(1/2x-3/4)^2-1/4=2`

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

`(1/2x-3/4)^2=9/4`

Trường hợp `1`.

`(1/2x-3/4)^2=(3/2)^2`

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

`1/2x=3/2+3/4`

`1/2x=9/4`

`x=9/4:1/2`

`x=9/2`.

Trường hợp `2`.

`(1/2x-3/4)^2=(-3/2)^2`

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

`1/2x=-3/2+3/4`

`1/2x=-3/4`

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

`x=-3/2`.

Vậy `x in{9/2;-3/2}`.

`d)` `(x+1)/2022+(x+2)/2021+(x+3)/2020=-3`

 `((x+1)/2022+1)+((x+2)/2021+1)+((x+3)/2020+1)=-3+3`

 `((x+1)/2022+2022/2022)+((x+2)/2021+2021/2021)+((x+3)/2020+2020/2020)=0`

 `(x+2023)/2022+(x+2023)/2021+(x+2023)/2020=0`

 `(x+2023)(1/2022+1/2021+1/2020)=0`

Vì `(1/2022+1/2021+1/2020)ne0`

Nên `x+2023=0`

`x=-2023`

Vậy `x=-2023`.