Đáp án `+` Giải thích các bước giải:

a) `x - 1/3 = (-2)/3`

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

`x = (-1)/3.`

b) `x : 0,75 = 2`

`x = 2 . 0,75`

`x = 1,5.`

c) `x + 2/3 = 35/21`

`x + 2/3 = 5/3`

`x = 5/3 - 2/3`

`x = 3/3`

`x = 1.`

d) `x - 1 = 7/12 + (-1)/3`

`x - 1 = 7/12 + (-4)/12`

`x - 1 = 3/12`

`x - 1 = 1/4`

`x = 1/4 + 1`

`x = 1/4 + 4/4`

`x = 5/4.`

f) `(3 - x)/15 = (-30)/75`

`(3 - x)/15 = (-2)/3`

`(3 - x) . 3 = (-2) . 15`

`(3 - x) . 3 = -30`

`3 - x = -30 : 3`

`3 - x = -10`

`x = 3 - (-10)`

`x = 3 + 10`

`x = 13.`

g) `(x + 2)/(-27) = (-3)/(x + 2)`

`(x + 2)(x + 2) = 3 . 27`

`(x + 2)^2 = 81`

TH1: `(x + 2)^2 = (-9)^2`

`x + 2 = -9`

`x = -9 - 2`

`x = -11.`

TH2: `(x + 2)^2 = 9^2`

`x + 2 = 9`

`x = 9 - 2`

`x = 7.`

Vậy: `x ∈ {7; -11}`

h) `5 . (3x - 1/2) + 1/4 = 5 1/4`

`5 . (3x - 1/2) + 1/4 = 21/4`

`5 . (3x - 1/2) = 21/4 - 1/4`

`5 . (3x - 1/2) = 20/4`

`5 . (3x - 1/2) = 5`

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

`3x - 1/2 = 1`

`3x = 1 + 1/2`

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

`3x = 3/2`

`x = 3/2 : 3`

`x = 3/2 . 1/3`

`x = 1/2.`

i) `3,75 - 2x = 0,25`

`2x = 3,75 - 0,25`

`2x = 3,5`

`x = 3,5 : 2`

`x = 35/10 . 1/2`

`x = 35/20`

`x = 7/4.`

k) `(4x - 1)(1,25x - 6) = 0`

TH1: `4x - 1 = 0`

`4x = 0 + 1`

`4x = 1`

`x = 1 : 4`

`x = 1/4.`

TH2: `1,25x - 6 = 0`

`125/100x - 6 = 0`

`5/4x - 6 = 0`

`5/4x = 0 + 6`

`5/4x = 6`

`x = 6 : 5/4`

`x = 6 . 4/5`

`x = 24/5.`

Vậy: `x ∈ {1/4; 24/5}`

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

`(1/3 + 2/3)x - 1 = 9/2`

`3/3x = 9/2 + 1`

`1x = 11/2`

`x = 11/2.`

m) `(x - (-5)/12) : 1 1/3 = 0,25`

`(x + 5/12) : 4/3 = 25/100`

`(x + 5/12) : 4/3 = 1/4`

`x + 5/12 = 1/4 . 4/3`

`x + 5/12 = 1/3`

`x = 1/3 - 5/12`

`x = 4/12 - 5/12`

x = (-1)/12.

n) `(0,6 - x)/(-2) = (-0,5)/(0,6 - x)`

`(0,6 - x) . (0,6 - x) = 2 . 0,5`

`(0,6 - x)^2 = 2 . 5/10`

`(0,6 - x)^2 = 1`

TH1: `(0,6 - x)^2 = 1^2`

`0,6 - x = 1`

`x = 0,6 - 1`

`x = -0,4`

TH2: `(0,6 - x)^2 = (-1)^2`

`0,6 - x = -1`

`x = 0,6 - (-1)`

`x = 0,6 + 1`

`x = 1,6.`