$\"\"$

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The sides of $\"\"$ are $\"\"$ , $\"\"$ and $\"\"$ .

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Using the Triangle Inequality Theorem, the sum of the lengths of any $\"\"$ sides of a triangle must be

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greater than the length of the remaining side this generates $\"\"$ inequalities to examine.

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Find the value of $\"\"$ .

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Consider the inequality is $\"\"$ .

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Case(i).

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$\"\"$ (First inequality)

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$\"\"$ (Commutative addition property: $\"\"$ )

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$\"\"$ (Combine like terms)

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$\"\"$ (Subtract $\"\"$ from each side)

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$\"\"$ (Apply additive inverse property: $\"\"$ )

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$\"\"$ (Subtract $\"\"$ from each side)

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$\"\"$ (Apply additive inverse property: $\"\"$ )

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Case(ii).

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$\"\"$ (Second inequality)

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$\"\"$ (Commutative addition property: $\"\"$ )

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$\"\"$ (Combine like terms)

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$\"\"$ (Subtract $\"\"$ from each side)

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$\"\"$ (Apply additive inverse property: $\"\"$ )

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$\"\"$ (Subtract $\"\"$ from each side)

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$\"\"$ (Apply additive inverse property: $\"\"$ )

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$\"\"$ (Divide each side by $\"\"$ )

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$\"\"$ (Cancel common terms)

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Case(iii).

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$\"\"$ (Third inequality)

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$\"\"$ (Commutative addition property: $\"\"$ )

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$\"\"$ (Combine like terms)

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$\"\"$ (Subtract $\"\"$ from each side)

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$\"\"$ (Apply additive inverse property: $\"\"$ )

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$\"\"$ (Subtract $\"\"$ from each side)

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$\"\"$ (Apply additive inverse property: $\"\"$ )

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$\"\"$ (Divide each side by $\"\"$ )

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$\"\"$ (Cancel common terms)

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In order for all $\"\"$ conditions to be true, $\"\"$ must be greater than $\"\"$ .

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$\"\"$

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A negative value will always be less than a positive value.