Let (k−1)x+2y≤6 be a linear inequality in two variables. It is known that the point (0,−1) satisfies the inequality while the point (3,4) does not.
a. (i) Obtain the inequality in k arising from the condition on (0,−1).
b. (ii) Obtain the inequality in k arising from the condition on (3,4).
c. (iii) Hence, find the range of values of k for which both conditions hold simultaneously.