(Rules for manipulating inequalities) Answer the following in parts
MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions
Problem
(Rules for manipulating inequalities) Answer the following in parts. Unless otherwise stated, x and y denote real numbers.
(a) State the effect, if any, on the sense (direction) of an inequality when both sides are multiplied or divided by:
(i) a positive real number, and (ii) a negative real number.
(b) Solve the inequality −3x+7>1 step by step, explicitly indicating at which stage (if any) the inequality sign changes. Give the final solution set on the number line.
(c) Without performing every arithmetic step, decide whether the inequality symbol in 5−2y≤9 will reverse or remain the same when both sides are multiplied by −4. Justify your answer briefly.