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Simplifying Using the Inverse Property
Simplify the expression by spotting additive inverses and using properties of real numbers:
Step 1 — Identify opposites: The first term and the third term are additive inverses of each other, because .
Step 2 — Reorder using the commutative property of addition: Swap the second and third terms so that the opposites are adjacent:
Step 3 — Apply the inverse property of addition: The pair sums to :
Step 4 — Apply the additive identity: Adding to any number leaves it unchanged:
The simplified result is . This example illustrates a practical simplification strategy: before adding left to right, scan the expression for terms that are opposites. Rearranging so that these terms sit next to each other allows them to cancel immediately, reducing the expression in fewer steps.
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Simplifying Using the Inverse Property
Simplifying Using the Inverse Property of Addition
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Learn After
In a corporate inventory ledger, the net change in units (n) is represented by the expression . Which mathematical property identifies that the sum of and is zero?
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A logistics analyst is simplifying a ledger balance represented by the expression . The analyst identifies that the sum of and is zero by applying the ____ Property of Addition.
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