Đáp án + Giải thích các bước giải:
`a) -1/4 + 1/4 : x = -5/8`
`⇒ 1/4 : x = -5/8 + 1/4`
`⇒ 1/4 : x = -5/8 + 2/8`
`⇒ 1/4 : x = -3/8`
`⇒ x = 1/4 : -3/8`
`⇒ x = 1/4 . -8/3`
`⇒ x = -2/3`
Vậy: `x = -2/3`
`b) |3/8 - x| + 5/6 = 7/4`
`⇒ |3/8 - x| = 7/4 - 5/6`
`⇒ |3/8 - x| = 21/12 - 10/12`
`⇒ |3/8 - x| = 11/12`
`+)` Với `x ≤ 3/8` thì:
`⇒ 3/8 - x = 11/12`
`⇒ x = 3/8 - 11/12`
`⇒ x = 36/96 - 88/96`
`⇒ x = -13/24`
`+)` Với `x ≥ 3/8` thì:
`⇒ x - 3/8 = 11/12`
`⇒ x = 11/12 + 3/8`
`⇒ x = 88/96 + 36/96`
`⇒ x = 31/24`
Vậy: `x = {-13/24 ; 31/24}`
`c) (2x - 1/3)^2 = (- 1/6)^2`
`⇒` $TH_1$: `2x - 1/3 = 1/6`
`⇒ 2x = 1/6 + 1/3`
`⇒ 2x = 1/6 + 2/6`
`⇒ 2x = 3/6 = 1/2`
`⇒ x = 1/2 : 2`
`⇒ x = 1/2 . 1/2`
`⇒ x = 1/4`
`⇒` $TH_2$: `2x - 1/3 = -1/6`
`⇒ 2x = -1/6 + 1/3`
`⇒ 2x = -1/6 + 2/6`
`⇒ 2x = 1/6`
`⇒ x = 1/6 : 2`
`⇒ x = 1/6 . 1/2`
`⇒ x = 1/12`
Vậy: `x = {1/4 ; 1/12}`
`d) (3^x - 1) + 5 . (3^x - 1) = 162`
`⇒ (3^x - 1) . (1 + 5) = 162`
`⇒ (3^x - 1) . 6 = 162`
`⇒ (3^x-1) = 27`
`⇒ (3^x - 1) = 3^3`
`⇔ x - 1 = 3`
`⇒ x = 4`
Vậy: `x = 4`
