Linear Inequality

Linear Inequality

 

A linear inequality in one variable can be written in the form

Ax +  B  <  C,

where A, B, and C are real numbers, with A ≠ 0.

 

Addition Property of Inequality

For all real numbers A, B, and C, the inequalities

A < B and A + C < B + C

are equivalent.

In words, adding the same number to each side of an inequality does not change the solution  set.

 

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.

 

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