Multiplication Property of Inequality and Solving a Linear Inequality

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.

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