Solve the following inequlaities
` 7x +15 ge 9 - 4x `
`-5 le ""(2-3x)/(4) le 9`
`5x- 6 le 4 " and " 7- 3x ge 2x`

Explanation

(i) `7x+15 ge 9- 4x`
Transferring - 4x from RHS to LHS and 15 from LHS to RHS , We get
` 7x + 4 x ge 9 - 15 `
`rArr 11x ge - 6`
`rArr x ge ""-6/11`
`rArr x in [ -6/11,oo)` ltbr. (ii) We have ,`-5 le (2-3x)/(4)le 9`
`rArr -20 ge 2- 3x le 36 `
`rArr -22 le - 3x le 34`
`rArr (22)/(3) ge x ge - (34)/(3)`
`rArr x in [(-34)/(3),(22)/(3)]`
(iii) we have `5x- 6 le 4 " and "7- 3x ge 2x`
`5x ge 7`
`rArr x le 7/3`
From (1) and (2) common value of x are `x gt 2 or x in (- oo , 2]`