The addition properties of inequality implies that the sign of the inequality does not change, when a common term is added to both sides of the inequality.
Both properties are addition properties of an inequality
Given that:
[tex]a > b \to a + c > b + c[/tex]
[tex]a < b \to a + b < b + c[/tex]
Notice that:
[tex]a > b[/tex]
When c is added to both sides
[tex]a + c > b + c[/tex]
The inequality sign remains the same
Also:
[tex]a < c[/tex]
When c is added to both sides
[tex]a + c < b + c[/tex]
The inequality sign remains the same
This implies that (a) and (b) are illustrations of addition property of inequality.
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