Đáp án+Giải thích các bước giải:
`5) (3x-1)/4-(3(x-2))/8-1 > (5-3x)/2`
`<=> (2(3x-1))/8-(3(x-2))/8-8/8 > (4(5-3x))/8`
`<=> 6x-2-3x+6-8 > 20-12x`
`<=> 3x-4 > 20 - 12x`
`<=> 15x > 24`
`<=> x > 8/5`
Vậy `S{x|x > 8/5}`
`6) (x-1)/(x-3) > 1`
`<=> (x-1)/(x-3) -1 > 0`
`<=> (x-1-x+3)/(x-1) > 0`
`<=> 2/(x-1) > 0`
`<=> x-1 > 0 `
`<=> x > 1`
Vậy `S={x| x > 1}`
`7) (2x-3)/(x+5) ≥ 3`
`<=> (2x-3)/(x+5) -3 ≥ 0`
`<=> (2x-3-3x-15)/(x+5) ≥ 0`
`<=> (-x-18)/(x+5) ≥ 0`
`<=>`$\left\{\begin{matrix}-x-18≥0\\ x + 5 > 0 \end{matrix}\right.$ hoặc $\left\{\begin{matrix}-x-18≤0\\ x + 5 < 0 \end{matrix}\right.$
`+)` $\left\{\begin{matrix}-x-18≥0\\ x + 5 > 0 \end{matrix}\right.$ `<=>` $\left\{\begin{matrix}x≤18\\ x > -5 \end{matrix}\right.$ `<=> -5 < x ≤ 18`
`+)` $\left\{\begin{matrix}-x-18≤0\\ x + 5 < 0 \end{matrix}\right.$`<=>` $\left\{\begin{matrix}x≥18\\ x < -5 \end{matrix}\right.$ `<=> -5 > x ≥ 18`(vô nghiệm)
Vậy `S={x|-5 < x ≤ 18}`
