Answer the following questions related to linear inequalities in one variable.
MATHEMATICS · Multi-part · CBSE · Mathematics · Linear Inequalities · Linear Inequalities
Problem
Answer the following questions related to linear inequalities in one variable.
(i) Define an inequality in one variable and its solution set.
(ii) 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. Explain, in words, why this reversal occurs.
(iii) Consider the statement −4x<12.
(a) Solve the inequality and write the solution set in interval notation.
(b) Verify by direct substitution whether x=−2 and x=−5 belong to the solution set and interpret the result in the context of your explanation in part (ii).