Đáp án `+` Giải thích các bước giải:

Bài `4:`

`1) x - 45 = 48 - 68`

`x - 45 = -20`

`x = -20 + 45`

`x=  25`

``

`2) 35 + 5 . ( 6 − x ) = ( − 12 ) + | − 112 |`

`35 + 5 (6 - x) = -12 + 112`

`35 + 5 (6 -x ) = 100`

`5 (6 - x) = 100 -35`

`5 (6-x) = 65`

`6 - x = 65 : 5`

`6 - x = 13`

`x = 6 - 13`

`x = -7`

``

`3) 126 - 3 [x - 9]`

`= 126 - 3x + 27`

`= (126 + 27)- 3x`

`= 153 - 3x`

``

`4) 157 - (x - 124)= -483`

`x- 124 = 157 + 483`

`x - 124 = 640`

`x = 640 + 124`

`x = 764`

``

`5) 46 - (3x - 2)^2 = (-38) + 20`

`46 - (3x - 2)^2 = -18`

`(3x-2)^2 = 46 + 18`

`(3x - 2)^2 = 64`

`3x - 2 = - 8` hoặc `3x - 2 = 8`

`3x = - 8 + 2`            `3x = 8 + 2`

`3x = -6`                     `3x = 10`

`x = -6 : 3`                `x = 10 : 3`

`x = -2`                         `x = 10/3`

Vậy `x \in {-2; 10/3}`

``

`6) 13 - | x + 6| = - 7 - 10`

`13 - |x + 6| = -17`

`|x + 6| = 13 + 17`

`| x+  6| = 30`

`x + 6 = -30` hoặc `x + 6 = 30`

`x = -30 - 6`          `x = 30 - 6`

`x = -36`               `x = 24`

Vậy `x \in {-36; 24}`

``

`7) (2x - 5)^3 = 15^2 - 4 . 5^2`

`(2x - 5)^3 = 225 - 4 . 25`

`(2x - 5)^3 = 225 - 100`

`(2x - 5)^3 = 125`

`2x - 5 = 5`

`2x = 5 + 5`

`2x = 10`

`x = 10 : 2`

`x = 5`

``

`8) |16 - x| - 4 = 18 - |12|`

`|16 - x| - 4 = 18 - 12`

`|16 - x| - 4= 6`

`|16 - x| = 6 + 4`

`|16 - x| = 10`

`16 - x = 10` hoặc `16 - x= -10`

`x= 16 - 10`            `x = 16 + 10`

`x=  6`                       `x = 26`

Vậy `x \in {6; 26}`

``

`9) (x-2)(15 - 3x) = 0`

`x - 2 = 0` hoặc `15 - 3x = 0`

`x = 2`                `3x = 15`

                         `x = 15 : 3`

                           `x = 5`

Vậy `x \in {2;5}`

``

`10) 117- (x+5) = 26 + (-9)`

`117 - (x+5) = 17`

`x + 5 = 117 - 17`

`x + 5 = 100`

`x = 100 - 5`

`x = 95`

``

`11) (x-5) - (2x + 7) = -8`

`x - 5 - 2x - 7 = - 8`

`(x - 2x) + (-5 - 7) = -8`

`-x - 12  = -8`

`-x = -8 + 12`

`-x = 4`

`x= -4`

``

`12) (x+1) + (x+2) + ... + (x  + 50) = 1 475`

`x + 1 + x + 2 + ... + x + 50 = 1475`

`(x + x+ ... + x) + (1+ 2 + ... + 50) = 1475`

Ta có: `1 + 2 + ... + 50 = (50 xx (50 + 1))/2 = 1275`

`=> 50x + 1275 = 1475`

`50x = 200`

`x = 200: 50`

`x = 4`

``

`13) x + (-36) = 33 - |-103|`

`x + (-36) = 33 - 103`

`x + (-36) = -70`

`x = -70 + 36`

`x = -34`

``

`14) [(8x - 12) : 4] . 3^6 = 3^9`

`(8x - 12) : 4 = 3^9 : 3^6`

`(8x - 12) : 4 = 3^3 = 27`

`8x - 12 = 27 . 4`

`8x - 12 = 108`

`8x = 108 + 12`

`8x = 120`

`x = 120 : 8`

`x = 15`

``

`15) 220 + [2^4 + (x-5)]= 8^2 . 5`

`220 + [16 + (x-5)] = 64 . 5`

`220+[16+(x−5)]=320`

`16 + (x-5) = 320 - 220`

`16 + (x-5) = 100`

`x - 5 = 100 -16`

`x  - 5 = 84`

`x = 84 + 5`

`x = 89`

``

`16) 213 − ( x − 6 ) = 2136 : 12`

`213 - (x - 6) = 178`

`x - 6 = 213 - 178`

`x - 6 = 35`

`x = 35 + 6`

`x = 41`

``

`17) 3 (2x -1)^3 - 1^2020 = 5 . 4^2`

`3 (2x - 1)^3 - 1 = 5 . 16`

`3 (2x - 1)^3 - 1 = 80`

`3 ( 2x - 1)^3 = 80 + 1`

`3 (2x - 1)^3 = 81`

`(2x- 1)^3 = 81 : 3`

`(2x-1)^3 = 27`

`2x - 1 = 3`

`2x = 3 + 1`

`2x=  4`

`x = 4 : 2`

`x = 2`

``

`18) 18 + | x + 7 | = 9 − ( − 11 )`

`18 + |x + 7| = 20`

`|x + 7| = 20 - 18`

`|x + 7| = 2`

`x + 7 = 2` hoặc `x + 7 =- 2`

`x = 2 - 7`            `x = -2 - 7`

`x = -5`                `x = -9`

Vậy `x \in {-5; -9}`

``

`19) − x + 5 = 3 x + ( − 11 )`

`-x - 3x = -5 - 11`

`-4x = -16`

`x = -16 : (-4)`

`x = 4`

``

`20) 2 x + 5 + ( x − 7 ) = ( − 3 ) + 22`

`2x + 5 + x - 7 = 19`

`(2x + x)+ (5 - 7) = 19`

`3x -2 = 19`

`3x = 19 + 2`

`3x = 21`

`x = 21 : 3`

`x = 7`

``

`21) ( x + 4 ) . ( 1 + | x − 2 | ) = 0`

`x + 4 = 0` hoặc `1 + |x - 2| = 0`

`x = -4`             `∣x−2∣≥0⇒1+∣x−2∣≥1 → x \in ∅`

Vậy `x = -4`