Answer the following with reference to linear inequalities in one variable:
MATHEMATICS · Multi-part · AoPS · Mathematics · Introduction to Inequalities · Introduction to Inequalities
Problem
Answer the following with reference to linear inequalities in one variable:
(i) State the rule that describes what happens to the direction of an inequality when both sides are multiplied or divided by a negative real number.
(ii) Write any inequality involving x that is true. Multiply both sides by −4 and explicitly show how the inequality symbol changes. Verify your final statement with one numerical value of x that satisfies it.
(iii) Solve the inequality −3(2x−5)>9. Express the solution set in interval notation and clearly indicate at which step the inequality symbol changed its direction.