4 (x-2) - 5x>-1

The sign is greater than or equal to

4 (x-2) - 5x>=-1

4x-8-5x>=-1

-x-8>=-1

-x>=7 here you can flip the signs

x>=-7

So x can be any number starting at - 7. so - 7, - 6, - 5, etc. 0, 1, 2, etc.

4 (x-2) - 5x>-1

First distribute the 4

4x-8-5x>-1

Then combine the like terms (the 4x and the - 5x)

-x-8>-1

Then add 8 to both sides

-x>7

Lastly divide each side by - 1, since you are dividing by a negative number the sign switches becoming less than

x<-7