Find all real numbers X such that 4x+2>14 AND - 21x+1>22

What you must do for this case is to solve both inequalities

We have then:

4x + 2> 14

We clear x:

4x + 2> 14

x> (14-2) / 4

x> 3

-21x + 1> 22

We clear x:

-21x> 22-1

x <-21/21

x <-1

Therefore we have to

For 4x + 2> 14

x belongs (3, inf)

For - 21x + 1> 22

x belongs (-inf, - 1)

The solution that is met for both inequalities is:

x belongs (-inf, - 1) U (3, inf)