To solve this, you need to isolate/get the variable "x" by itself in the inequality:
2(1 - x) > 2x Divide 2 on both sides
[tex]\frac{2(1-x)}{2} >\frac{2x}{2}[/tex]
1 - x > x Add x on both sides to get "x" on one side of the inequality
1 - x + x > x + x
1 > 2x Divide 2 on both sides to get "x" by itself
[tex]\frac{1}{2} >x[/tex] or [tex]x<\frac{1}{2}[/tex] (x is any number less than 1/2)
[Another way you could've solved it]
2(1 - x) > 2x Distribute 2 into (1 - x)
(2)1 + (2)(-x) > 2x
2 - 2x > 2x Add 2x on both sides
2 - 2x + 2x > 2x + 2x
2 > 4x Divide 4 on both sides to get "x" by itself
[tex]\frac{2}{4} >\frac{4x}{4}[/tex]
[tex]\frac{1}{2} >x[/tex]
