Question

How do you solve compound inequalities `4x + 7 < 11 or 1 – x ≤ -2`?

Answer 1

Initially treat the two inequalities separately

`4x+7<11`
`4x<4`
`x<1`

`1-x<=-2`
`1<=x-2`
`3<=x`

Combine as a compound condition
`4x+7<11 " or " 1-x<=-2`
`rarr`
`x<1 " or " x>=3`

`x epsilon (-oo,1) uu [3,+oo)`