Solve for x in the inequality (2x-1) / 3 > 1. Cite an axiom, definition or theorem at each step. Show the solution set on the number line.

First, we'll subtract 1 both
sides:

(2x-1)/3 - 1 >
0

We'll multiply 1 by 3:

(2x -
1 - 3)/3 > 0

We'll combine like terms within
brackets:

(2x-4)/3 >
0

A fraction is positive if both, numerator and
demominator, have the same sign.

Since the denominator of
the fraction, namely 3, is positve, therefore, to keep the sense of the inequality, the
numerator must be also positive:

2x - 4 >
0

We'll add 4 both sides, to isolate 2x to the
left:

2x > 4

We'll
divide by 2 both sides and the sense of inequality holds:

x
> 4/2

x >
2

The values of x, for the inequality holds,
belong to the opened interval (2 ; +`oo` ).