We are given that $$a < b$$. Compare the following pairs: a) $$21a$$ and $$21b$$; b) $$-3.2a$$ and $$-3.2b$$; c) $$1.5b$$ and $$1.5a$$.

Solution:

We are given that $$a < b$$.

• a) Comparing $$21a$$ and $$21b$$:
  Since we are multiplying both sides of the inequality $$a < b$$ by a positive number (21), the inequality sign remains the same.
  Therefore, $$21a < 21b$$.
• b) Comparing $$-3.2a$$ and $$-3.2b$$:
  When we multiply or divide both sides of an inequality by a negative number, the inequality sign reverses.
  Therefore, $$-3.2a > -3.2b$$.
• c) Comparing $$1.5b$$ and $$1.5a$$:
  We can rewrite $$1.5b$$ and $$1.5a$$ as $$1.5 imes b$$ and $$1.5 imes a$$. Since we are multiplying both sides of the inequality $$a < b$$ by a positive number (1.5), the inequality sign remains the same.
  Therefore, $$1.5a < 1.5b$$.

Answer:

• a) $$21a < 21b$$
• b) $$-3.2a > -3.2b$$
• c) $$1.5a < 1.5b$$