Answer the following questions on compound inequalities.
MATHEMATICS · Multi-part · CBSE · Mathematics · Linear Inequalities · Linear Inequalities
Problem
Answer the following questions on compound inequalities.
(i) Define the intersection of the solution sets of two linear inequalities in one variable and illustrate your definition with a short numerical example.
(ii) Justify why, in the inequality a<b, multiplying both sides by a negative real number k(k<0) reverses the direction of the inequality sign.
(iii) Solve the compound inequality −4<−2(3x−5)≤8, clearly indicating the step at which the inequality signs change, and write the final solution set in interval notation.
(iv) Represent the solution obtained in part (iii) on a number line, marking open or closed points as required.