Đáp án + Giải thích các bước giải:
`a) (x - 1)/4 + (2x - 3)/6 = (-7x + 1)/8 <=> [6(x - 1)]/24 + [4(2x - 3)]/24 = [3(-7x + 1)]/24` $\\$ `<=> [6(x - 1) + 4(2x - 3)]/24 = [-21x + 3]/24 <=> 6(x - 1) + 4(2x - 3) = -21x + 3` $\\$ `<=> 6x - 6 + 8x - 12 + 21x - 3 = 0 ` $\\$ `<=> 35x-21 = 0 <=> x = 21/35 = 3/5`
Vậy `S = {3/5}`
`b) (x - 5)/6 + (x + 5)/10 = (x - 1)/5 <=> [5(x - 5)]/30 + [3(x + 5)]/30 = [6(x - 1)]/30` $\\$ `<=>[5(x - 5) + 3(x + 5)]/30 = [6(x - 1)]/30` $\\$ `<=> 5(x - 5) + 3(x + 5) = 6(x - 1)` $\\$ `<=> 5x - 25 + 3x + 15 = 6x - 6` $\\$ `<=> 5x - 25 + 3x + 15 - 6x + 6 = 0 <=> 2x - 4 = 0 <=> x = 2`
Vậy `S = {2}`
`c) (x + 3)/4 - (x - 2)/10 = (x + 1)/20 <=> [5(x + 3)]/20 - [2(x - 2)]/20 = (x + 1)/20` $\\$ `<=> [5(x + 3) - 2(x - 2)]/20 = (x + 1)/20` $\\$ `<=> 5(x + 3) - 2(x - 2) = x + 1 <=> 5x + 15 - 2x + 4 - x - 1 = 0` $\\$ `<=> 2x + 18 = 0 <=> x = -9`
Vậy `S = {-9}`
`d) (4x - 1)/18 - (3x + 2)/9 = (x - 1)/4 <=> [2(4x - 1)]/36 - [4(3x + 2)]/36 = [9(x - 1)]/36` $\\$ `<=> [2(4x - 1) - 4(3x + 2)]/36 = [9(x - 1)]/36` $\\$ `<=> 2(4x - 1) - 4(3x + 2) = 9(x - 1)` $\\$ `<=> 8x - 2 - 12x - 8 = 9x - 9 <=> 8x - 12x - 9x = -9 + 8 + 2` $\\$ `<=> -13x = 1 <=> x = -1/13`
Vậy `S = {-1/13}`
`e) (-7x + 6)/5 - (x - 8)/10 = (2x + 8)/4 <=> [4(-7x + 6)]/20 - [2(x - 8)]/20 = [5(2x + 8)]/20` $\\$ `<=> [4(-7x + 6) - 2(x - 8)]/20 = [5(2x + 8)]/20` $\\$ `<=> 4(-7x + 6) - 2(x - 8) = 5(2x + 8)` $\\$ `<=> -28x + 24 - 2x + 16 = 10x + 40 <=> -28x - 2x - 10x = 40 - 16 - 24` $\\$ `<=> -40x = 0 <=> x = 0`
Vậy `S = {0}`
`f) (3x - 7)/12 + (5x - 5)/15 = (x + 15)/10 + (3x + 5)/20` $\\$ `<=> [5(3x - 7)]/60 + [4(5x - 5)]/60 = [6(x + 15)]/60 + [3(3x + 5)]/60` $\\$ `<=> [5(3x - 7) + 4(5x - 5)]/60 = [6(x + 15) + 3(3x + 5)]/60` $\\$ `<=> 5(3x - 7) + 4(5x - 5) = 6(x + 15) + 3(3x + 5)` $\\$ `<=> 15x - 35 + 20x - 20 = 6x + 90 + 9x + 15` $\\$ `<=> 15x + 20x - 6x - 9x = 15 + 90 + 20 + 35 <=> 20x = 160 <=> x = 8`
Vậy `S = {8}`