Find the values of x which satisfy the following inequalities simultaneously:
(a) `-3 lt 2x -1 lt 19 `
(b ) ` -1 le (2x+3)/(5) le 3 `

Answer

(-1,6]

Explanation

`-3 lt 2x - 1 lt 19`
`or -2 lt 2x lt 20 `
`or -1 lt x lt 10 `
`-1 le (2x+3)/(5) le 3`
`or -5 le 2 x +3le 15`
`or -8 le 2x le 12`
`or -4 le x le 6 `
Now from ( 1) and ( 2) common values are (-1 , 6)