−4x − 6 < x + 9

why cant we do it like this:

-4x-x<9+6

-5x<15

x<-15/5

x<-3

 

 why is there a need of these rules ?

 Look at the fact 2 < 3

You can add or subtract the same quantity from both sides and the inequality remains the same

e. g. subtracting 5 from each side, we get

2 - 5 < 3 - 5

-3  <  -2 which implies (read in the reverse direction)

-2  >  -3

So 2 < 3 implies -2 > -3

This means whenever we change sign on each side, the inequality is reversed (< becomes > and > becomes <)

Now refer to your solution:

Upto the step -5x < 15 it is OK

As per the above rule we should have 5x > -15

Now let us remember another fact:

By multiplying or dividing by the same positive quantity on both sides of an inequality, the (existing) sign is unchanged

So your next step should be 5x / 5 > -15 / 5

Hence x > -3