Question

How do you solve `x + 4 < 2` or `x - 4 > -1`?

Answer 1

To solve linear inequalities the very first step is to take the like terms on one side of the inequality.

`x+4<2`

So, to solve the first inequality we can see that constants are the two like terms that is why, we will take the constants to one side.

• `x<2-4`
  As, we are taking 4 to the other side this +4 will become - 4 because we apply the inverse operation and the inverse operation of addition is subtraction. That is why, when we take the +4 to other side it will become -4.

• `x<-2`

For solving the next inequality again we will take the like terms to one side so our inequality will look something like this:-
`x> - 1+4`
The -4 became a positive 4 because when we take any quantity from one side to the other we apply the inverse operation. As inverse operation of addidition is subtraction +4 became -4.This will be,-
`x>3`
The answer will be +3 and not a -3 because we apply the operation of the bigger number in the answer. As, 4 >1 that is why the answer is a +3.