Mathematics

Problem

Let

a

be a real parameter. Solve the inequality

(a+2)x-5 \ge (3a-1)x+4

with respect to

x

. a. (i) Obtain the solution set for

x

in terms of

a

, clearly distinguishing the cases arising from the sign of the coefficient of

x

after simplification. b. (ii) For which values of

a

is the inequality true for every real number

x

? Justify your answer. c. (iii) For which value(s) of

a

does the inequality have no solution? Give reasons for your conclusion.