Here is a summary of some inequality rules.
Fill in the blanks to complete the rules. (The first rule is already complete.)
You can add or subtract the same quantity from both sides.
You can multiply/divide both sides by a number.
You can multiply/divide both sides by a number if you flip the inequality sign.
if a < b and b < c and a < b and c < d and 0 < a < b and 0 < c < d and n is positive or negative then ac bd a^n b^n
if a < b and b < c, then a < c (transitive property of inequalities)
if a < b and c < d, then a+c < b+d (adding inequalities)
if a < b and n is positive, then an < bn (multiplying by a positive number preserves the inequality)
if a < b and n is negative, then an > bn (multiplying by a negative number flips the inequality sign)
Therefore, ac < bc (multiplying both sides by c)
and
bd < cd (multiplying both sides by d)
and
a^n < b^n (if n is positive)
and
a^n > b^n (if n is negative)