Identify the property illustrated in each statement. Assume all variables represent real numbers. (t-6)∙(1/t-6)=1, if t-6 ≠ 0

검증된 단계별 안내

First, observe the given expression: \((t-6) \times \left( \frac{1}{t-6} \right) = 1\), with the condition that \(t-6 \neq 0\) to avoid division by zero.

Recognize that multiplying a number by its reciprocal results in 1. Here, \((t-6)\) is multiplied by its reciprocal \(\frac{1}{t-6}\).

This illustrates the Multiplicative Inverse Property, which states that for any nonzero number \(a\), \(a \times \frac{1}{a} = 1\).

The condition \(t-6 \neq 0\) ensures that the reciprocal \(\frac{1}{t-6}\) is defined, which is necessary for the property to hold.

Therefore, the property illustrated by the equation is the Multiplicative Inverse Property.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Multiplicative Inverse Property

This property states that for any nonzero real number a, multiplying a by its reciprocal 1/a results in 1. In the given expression, (t-6) and (1/(t-6)) are multiplicative inverses, so their product equals 1, provided t-6 ≠ 0.

Domain Restrictions

Domain restrictions specify values that variables cannot take to avoid undefined expressions. Here, t-6 ≠ 0 ensures the denominator in 1/(t-6) is not zero, preventing division by zero and making the expression valid.

Properties of Real Numbers

These are fundamental rules governing operations with real numbers, including multiplication and division. Understanding these properties helps identify and justify equalities like the one given, ensuring the expression follows algebraic rules.