Answer the following questions based on the fundamental properties of inequalities.
a. (i) Prove that if a<b and c<0, then ca>cb. Give a logical justification for the reversal of the inequality sign.
b. (ii) Show that adding the same real number k to both sides of an inequality does not alter its direction. Illustrate your reasoning with a general proof for a<b⇒a+k<b+k.
c. (iii) Using the results of parts (i) and (ii), transform the inequality −4x+3>11 step by step until x is isolated, and state the final solution set for x.