1 - x > x - 1

[frenchyff]

1 - x > x - 1

i know this is the same as x < 1 but i am not sure how this was derived from 1 - x > x - 1

any help on understanding this would be great.

thanks in advance

 

[Romsek]

1 - x > x - 1

i know this is the same as x < 1 but i am not sure how this was derived from 1 - x > x - 1

any help on understanding this would be great.

thanks in advance

1-x > x-1

2 > 2x

1 > x

if you want to go the other way

x < 1

2x < 2

x + x < 1 + 1

x-1 < 1-x

 

[HallsofIvy]

1 - x > x - 1

i know this is the same as x < 1 but i am not sure how this was derived from 1 - x > x - 1

any help on understanding this would be great.

thanks in advance

You can solve inqualities almost exactly like you solve equations:
You can add or subtract the same thing from both sides and still have a true inequality.
You can multiply or divide both sides by the same positive number and still have a true inequality.
If you multiply or divide both sides by the same negative number you have to reverse the inequality.

How would you solve 1- x= x- 1? How do you change that to solve the inequaity?