`\text{~~Holi~~}`
`1.`
`x^3-6x^2-7x-5<(x-2)^3`
`-> x^2-6x^2-7x-5<x^3-6x^2+12x-8`
`-> -7x-5<12x-8`
`-> -7x-12x<-8+5`
`-> -19x<-3`
`-> x>3/(19)`
`2.`
`x^2<(x+2)^2`
`-> x^2<x^2+4x+4`
`-> 0<4x+4`
`-> -4x<4`
`-> x>-1`
`3.`
`3-\dfrac{4x-1}{18}>\dfrac{x-1}{12}-\dfrac{4-5x}{9}`
`-> 108-2(4x-1)>3(x-1)-4(4-5x)`
`-> 108-8x+2>3x-3-16+20x`
`-> 110-8x>23x-19`
`-> -8x-23x-19-110`
`-> -31x> -129`
`-> x<(129)/(31)`
`4.`
`(2x-3)(x+3)\ge0`
`->`\(\left[ \begin{array}{l}\begin{cases}2x-3\ge0\\x+3\ge0\end{cases}\\\begin{cases}2x-3\le0\\x+3\le0\end{cases}\end{array} \right.\)
`->`\(\left[ \begin{array}{l}\begin{cases}x\ge\dfrac{3}{2}\\x\ge-3\end{cases}\\\begin{cases}x\le\dfrac{3}{2}\\x\le-3\end{cases}\end{array} \right.\)
`->`\(\left[ \begin{array}{l}x\in[\dfrac{3}{2},+∞)\\x\in(-∞,-3]\end{array} \right.\)
`-> x\in∈(-∞,-3]∪[3/2,+∞)`
`5.`
`(3x-1)/4-(3(x-2))/8-1>(5-3x)/2`
`-> (3x-1)/4-(3x-6)/8-1>(5-3x)/2`
`-> 2(3x-1)-(3x-6)-8>4(5-3x)`
`-> 6x-2-3x+6-8>2x-12x`
`-> 3x-4>20-12x`
`-> 3x+12x>20+4`
`-> 15x>24`
`-> x>8/5`
