Đáp án+Giải thích các bước giải:
`a) 2(x+1)-3(x-2)=x-2`
`<=> 2x+2-3x+6=x-2`
`<=> -x + 8 = x - 2`
`<=> -2x = -10`
`<=> x = 5`
Vậy `S={5}`
`b) 3/x+(2x+1)/(x-3)+(x^2+12)/(3x-x^2)=0`
`<=>3/x+(2x+1)/(x-3)-(x^2+12)/(x^2-3x)=0`
`<=> 3/x+(2x+1)/(x-3)-(x^2+12)/(x(x-3))=0`
`<=> (3(x-3))/(x(x-3))+(x(2x+1))/(x(x-3))-(x^2+12)/(x(x-3))=0`
`=> 3x-9+2x^2+x-x^2-12=0`
`<=> x^2+4x-21=0`
`<=> (x-3)(x+7)=0`
`<=>`\(\left[ \begin{array}{l}x-3=0\\x+7=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=3\\x=-7\end{array} \right.\)
Vậy `S={3; -7}`
`c) x(x+1)-2x ≥ (x-2)^2`
`<=> x^2+x-2x ≥ x^2-4x+4`
`<=>-x ≥ -4x+4`
`<=> 3x ≥ 4`
`<=> x ≥ 4/3`
Vậy `S={x|x≥ 4/3}`
`d) (x-2)/3-(2x+2)/8 < 1 + (1+5x)/(12)`
`<=> (8(x-2))/(24)-(3(2x+2))/(24) < 24+ (2(1+5x))/(24)`
`<=> 8x -16 - 6x - 6 < 24 + 2 + 10x`
`<=> 2x - 22 < 26 +10x`
`<=> -8x < 48`
`<=> x > -6`
Vậy `S={x|x > -6}`
