Textbook Question
Let A = { -6, - 12/4 , - 5/8 , - √3, 0, 1/4 , 1, 2π, 3, √12}. List all the elements of A that belong to each set. Integers
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0. Review of Algebra
Exponents
1:36 minutesProblem 115
Textbook Question
Identify the property illustrated in each statement. Assume all variables represent real numbers. (t-6)∙(1/t-6)=1, if t-6 ≠ 0
Verified step by step guidance1
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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Video duration:
1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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.
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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.
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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.
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