Đáp án + Giải thích các bước giải:
a) `3x - 8 = 2(x - 4) + 5` $\\$ `<=> 3x-8=2x-8+5` $\\$ `<=>3x-8-2x+8-5=0` $\\$ `<=>x - 5 = 0 <=> x = 5`
Vậy `S = {5}`
b) `x^2 + 5x - 6 = 0` $\\$ `<=> x^2-x + 6x - 6 = 0` $\\$ `<=> x(x - 1) + 6(x - 1) = 0` $\\$ `<=> (x - 1)(x + 6) = 0 <=> `\(\left[ \begin{array}{l}x=1\\x=-6\end{array} \right.\)
Vậy `S = {1;-6}`
c) `3/(x + 1) - 2/(x - 2) = (4x - 2)/[(x + 1)(x - 2)](x ne -1,x ne 2)` $\\$ `<=> [3(x - 2)]/[(x+1)(x-2)] - [2(x+1)]/[(x+1)(x-2)] = (4x - 2)/[(x + 1)(x - 2)]` $\\$ `=> 3(x - 2) - 2(x + 1) = 4x - 2` $\\$ `<=> 3x - 6 - 2x - 2 - 4x + 2 = 0` $\\$ `<=> -3x - 6 = 0` $\\$ `<=> -3x = 6 <=> x = -2(TMĐK)`
Vậy `S = {-2}`
d) `|2x - 5| = x + 2`
`<=> `\(\left[ \begin{array}{l}2x-5=x+2\\-(2x-5)=x+2\end{array} \right.\) $\\$ `<=> ` \(\left[ \begin{array}{l}2x-5-x-2=0\\-2x+5-x-2=0\end{array} \right.\) $\\$ `<=> ` \(\left[ \begin{array}{l}x-7=0\\-3x + 3 = 0\end{array} \right.\) $\\$ `<=> `\(\left[ \begin{array}{l}x=7\\x = 1\end{array} \right.\)
Vậy `S = {7;1}`
