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- The additive inverse property is essential in applying the Division and Multiplication Properties of Equality when solving equations. When solving an equation like $3x + 2 = 11$, we can isolate the variable $x$ by subtracting $2$ from both sides, using the additive inverse property: $3x + 2 - 2 = 11 - 2$, which simplifies to $3x = 9$.
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What is an Additive inverse? An additive inverse of a number is defined as the value, which on adding with the original number results in zero value. It is the value we add to a number to yield zero. Suppose, a is the original number, then its additive inverse will be minus of a i.e.,-a, such that; a+(-a) = a – a = 0. Example: Additive ...
Additive inverse of a number is a number that, when added to the original number, gives the sum of 0. Learn the definition, property, formula, and more.
- The additive inverse of 0 is 0 itself.
- Except for 0, the additive inverse of all other whole numbers (natural numbers) is always negative, since all the natural numbers are positive.
- The sum of a number and its additive identity is the number itself, whereas the sum of a number and its additive inverse is 0.
Additive inverse is what you add to a number to make the sum zero. For example, the additive inverse of 4 is -4 because their sum is zero. When two numbers are added together to get 0, then we say both the numbers are additive inverses of each other.
May 28, 2023 · Definition: Inverse Properties. Inverse Property of Addition for any real number a, \[a + (−a) = 0\] −a is the additive inverse of a. Inverse Property of Multiplication for any real number a ≠ 0, \[a \cdot \dfrac{1}{a} = 1\] \(\dfrac{1}{a}\) is the multiplicative inverse of a.
An inverse property is two properties that undo each other e.g. addition and subtraction or multiplication and division. You can perform the same inverse property on each side of an equivalent equation without changing the equality.
The additive inverse demonstrates the property of cancellation; for example, if a + b = a + c, then b must equal c if 'a' is not equal to zero. Understanding additive inverses is crucial when solving equations since they allow for isolating variables by adding the inverse to both sides.
For example, when solving an equation like $x + 5 = 12$, we can subtract $5$ from both sides to isolate the variable $x$ by using the additive inverse property: $x + 5 - 5 = 12 - 5$, which simplifies to $x = 7$. Analyze how the additive inverse property is utilized when solving equations using the Division and Multiplication Properties of Equality.
