If 3x-1 is greater than zero then;

3x-1 >0 ------(a)

the associated equation is;

3x-1= 0

3x=1

x=1/3

so, equation (a) is satisfies only when x>1/3

so the solution for (a) is ]1/3 +infinity[

If 3x-1 is less than zero then;

3x-1<0 ------(b)

then associated equation is;

3x-1=0

x=1/3

equation (b) is satisfies only when x< 1/3

so solution is ]-infinity 1/3]

so, the solution for inequality 3x-1 is ]-infinity +infinity[

3x-1 >0 ------(a)

the associated equation is;

3x-1= 0

3x=1

x=1/3

so, equation (a) is satisfies only when x>1/3

so the solution for (a) is ]1/3 +infinity[

If 3x-1 is less than zero then;

3x-1<0 ------(b)

then associated equation is;

3x-1=0

x=1/3

equation (b) is satisfies only when x< 1/3

so solution is ]-infinity 1/3]

so, the solution for inequality 3x-1 is ]-infinity +infinity[