The inequality is .

Apply subtraction property of inequality: If then .

Subtract b from each side.

. Here we have two cases.

Case 1:If  a is positive then apply division property of inequality: if then .

Divide each side by a.

. This is solution 1.

Case 2:If a is negative then apply division property of inequality: if then .

Divide each side by a and reverse the inequality.

. This is solution 2.

Condition 1: .

For example the values of and substitute these values in the solution 1.

. \ \

Therefore the all solutions are not positive in condition 1.

Condition 2: .

For example the values of and substitute these values in the solution 2.

. \ \

Therefore the all solutions are not positive in condition 2.

Condition 3: .

For example the values of and substitute these values in the solution 1.

. \ \

Therefore the all solutions are positive in condition 3.

Condition 4: .

For example the values of and substitute these values in the solution 2.

. \ \

Therefore the all solutions are positive in condition 4.

The option C is correct answer.