Write true (T) or false (F) : (i) (2/3)x -(4/5) ≥ 8 is an inequation. (ii) If a b and m 0, then . (iii) If a b, m 0, then a - m b - m. (iv) If a b and m 0, then am bm. (v) If a b and m 0, then .

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KnowledgeBoat · Accepted Answer

(i) True Reason — Any mathematical statement that uses inequality symbols like , , , or to compare two expressions is defined as an inequation. (ii) True Reason — This follows the Negative Division Rule. When we divide both sides of an inequality by a negative number (m 0), the direction of the inequality sign must be reversed ( becomes ). (iii) False Reason — Adding or subtracting any number (whether positive or negative) from both sides of an inequality never changes the direction of the sign. If a b, then a - m b - m remains true regardless of the value of m. (iv) True Reason — Similar to the division rule, multiplying by a negative number (m 0) requires flipping the sign. (v) False Reason — When we divide by a positive number (m 0), the inequality sign stays the same. Therefore, if a b, the result should be .

Mathematics

Write true (T) or false (F) : (i) (2/3)x -(4/5) ≥ 8 is an inequation. (ii) If a b and m 0, then . (iii) If a b, m 0, then a - m b - m. (iv) If a b and m 0, then am bm. (v) If a b and m 0, then .

Linear Inequations

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