Fill in the blanks :

(i) A statement of inequality between two expressions is called an …………… .

(ii) The set from which the values of the variable satisfying a given inequality are chosen, is called the …………… .

(iii) Subset of the replacement set, consisting of all those values of the variable which satisfy the given inequation is called the …………… .

(iv) Multiplying each side of an inequality by a negative number, …………… the inequality.

(v) If a ≠ 0, b ≠ 0 and a < b, then $\dfrac{1}{a}$ …………… $\dfrac{1}{b}$.

(i) A statement of inequality between two expressions is called an inequation.

(ii) The set from which the values of the variable satisfying a given inequality are chosen, is called the replacement set.

(iii) Subset of the replacement set, consisting of all those values of the variable which satisfy the given inequation is called the solution set.

(iv) Multiplying each side of an inequality by a negative number, reverses the inequality.

(v) If a ≠ 0, b ≠ 0 and a < b, then $\dfrac{1}{a}$ > $\dfrac{1}{b}$.

Explanation

(i) While an "equation" uses an equals sign (=), a statement using symbols like <, >, ≤, or ≥ is termed an inequation.

(ii) Replacement set is the "universe" of numbers (like Natural numbers N or Integers Z) from which you are allowed to pick potential answers.

(iii) Solution set is the specific group of numbers that actually make the inequation true. It is always a subset of the replacement set.

(iv) Multiplying by a negative value changes the direction of the sign (> becomes <). This is the most important rule in inequalities.

(v) For non-zero numbers, taking the reciprocal reverses the inequality. This is the Reciprocal Rule.

For example, if 2 < 5, then $\dfrac{1}{2}$ > $\dfrac{1}{5}$ (0.5 > 0.2).