Identify the property illustrated in each statement. Assume all variables represent real numbers. (t-6)*(1/t-6)=1, if t-6 not equal to 0
Verified step by step guidance
1
Identify the expression: .
Recognize that the expression involves multiplication of a number and its reciprocal.
Recall the property: The multiplicative inverse property states that for any non-zero real number , .
Apply the property: Here, , and , so illustrates the multiplicative inverse property.
Note the condition: The property holds as long as , ensuring is not zero, which would make the reciprocal undefined.
Recommended similar problem, with video answer:
Verified Solution
This video solution was recommended by our tutors as helpful for the problem above
Video duration:
1m
Play a video:
Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Properties of Real Numbers
Real numbers possess specific properties, such as the commutative, associative, and distributive properties. These properties govern how numbers interact in operations like addition and multiplication. Understanding these properties is essential for manipulating algebraic expressions and solving equations.
The Zero Product Property states that if the product of two factors equals zero, at least one of the factors must be zero. This property is crucial when solving equations, as it allows us to set each factor to zero to find possible solutions. In the given statement, it helps in understanding the conditions under which the equation holds true.
Reciprocal relationships involve pairs of numbers whose product is one. For any non-zero number 'a', its reciprocal is '1/a'. In the context of the given equation, recognizing that (t-6) and 1/(t-6) are reciprocals helps in simplifying the expression and understanding the conditions under which the equation is valid.