Sketch the region in which the points satisfying the following inequality lie.
`(i)2x-3y-5 gt 0 " (ii) " -3x+4y+7 gt 0`
`(iii)x gt 2 " (iv) " y gt -3`

Explanation

`(i)2x -3y-5 gt 0`
`" Let " L(x,y) = 2x-3y-5`
`L(0,0) = -5 lt 0`
` "So," 2x-3y-5 gt 0` represents the half origin of the plane where origin does not lie, i.e., below line 2x-3y-5=0.

`(ii) -3x+4y+7 gt 0`
Let L(x,y) = -3x+4y+7
`L(0,0) = 7 gt 0`
`" SO, " -3x+4y+7 gt 0` represents the half region of the plane where origin lies, i.e., above line -3x+4y+7=0.


`(iii) x gt 2 or x-2 gt 0`
Let L(x,y) = x-2
`L (0,0) = 0-2 lt0`
` "So, " x-2 gt 0` represents the half region of the plane where origin does not lie, i.e., the right of the line x=2.
`(iv) y gt -3 or y+3 gt 0`
Let L(x,y) = y+3
`L(0,0)=0+3 gt 0`
`So, y+3 gt 0` represents the half region of the plane where origin lies, i.e., above the line y+3=0.