Multiplication Property of Inequality
For all real numbers A, B, and C, with C Z 0,
(a) the inequalities
A < B and AC < BC
are equivalent if C > 0;
(b) the inequalities
A < B and AC >BC
are equivalent if C < 0.
In words, each side of an inequality may be multiplied (or divided)
by a positive number without changing the direction of the inequality
symbol. Multiplying (or dividing) by a negative number requires that
we reverse the inequality symbol.
Solving a Linear Inequality
Step 1 Simplify each side separately. Use the distributive property to
clear parentheses and combine like terms as needed.
Step 2 Isolate the variable terms on one side. Use the addition property
of inequality to get all terms with variables on one side of
the inequality and all numbers on the other side.
Step 3 Isolate the variable. Use the multiplication property of
inequality to change the inequality to the form x <k or x > k.