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

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

`=> x = 5/10 - 4/10`

`=> x = 1/10`

b) `1/3 + 2/3 : x = 2`

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

`=> 2/3 : x = 6/3 - 1/3`

`=> 2/3 : x = 5/3`

`=> x = 2/3 : 5/3`

`=> x = 2/3 xx 3/5`

`=> x = 2/5`

c) `21 + (25 - 2 xx x) : 3 = 26`

`=> (25 - 2 xx x) : 3 = 26 - 21`

`=> (25 - 2 xx x) : 3 = 5`

`=> 25 - 2 xx x = 5 xx 3`

`=> 25 - 2 xx x = 15`

`=> 2 xx x = 25 - 15`

`=> 2 xx x = 10`

`=> x = 10 : 2`

`=> x = 5`

d) `(x- 2024)/2025 = 1/675`

`=> (x - 2024)/2025 = 3/2025`

`=> x - 2024 = 3`

`=> x = 3 + 2024`

`=> x = 2027`

e) `2/3 < x xx [(1/6 + 2/15 + 3/40 + 4/96) : 5] < 5/6`

`=> 4/6 < x xx [(1/2 - 1/3 + 1/3 - 1/5 + 1/5 - 1/8 + 1/8 - 1/12 ): 5] < 5/6`

`=> 4/6 < x xx [(1/2 - 1/12) : 5] < 5/6`

`=> 4/6 < x xx [5/6 : 5] < 5/6`

`=> 4/6 < x xx 1/6 < 5/6`

`=> 4/6 < x/6 < 5/6`

`=> 4 < x < 5`