Questions: Choose the property of addition that justifies the equation. 0 = -5 + 5

Choose the property of addition that justifies the equation. 0 = -5 + 5
Transcript text: Choose the property of addition that justifies the equation. \[ 0=-5+5 \]
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Solution

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Solution Steps

To determine the property of addition that justifies the equation \(0 = -5 + 5\), we need to recognize that adding a number and its additive inverse (opposite) results in zero. This is known as the Additive Inverse Property.

Step 1: Identify the Equation

We start with the equation: \[ 0 = -5 + 5 \]

Step 2: Apply the Additive Inverse Property

The Additive Inverse Property states that for any number \( a \), the equation \( a + (-a) = 0 \) holds true. In this case, we have: \[ -5 + 5 = 0 \] This confirms that the sum of a number and its additive inverse equals zero.

Step 3: Verify the Result

We can verify that: \[ -5 + 5 = 0 \] is indeed true, which justifies the equation \( 0 = -5 + 5 \).

Final Answer

The equation \( 0 = -5 + 5 \) is justified by the Additive Inverse Property. Thus, the answer is: \[ \boxed{\text{Additive Inverse Property}} \]

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