Is this equation an identity?
[tex]11.21+11.9 k=11.9 k+11.21[/tex]
Answer:
yes
no
Answer (2)
Apply the commutative property of addition to rewrite the right side of the equation.
Compare the left side and the right side of the equation.
Since the left side is equal to the right side for all values of k , the equation is an identity.
The equation is an identity, so the answer is yes .
Explanation
Understanding the Problem We are given the equation 11.21 + 11.9 k = 11.9 k + 11.21 and asked to determine if it is an identity. An identity is an equation that is true for all values of the variable k .
Applying Commutative Property To check if the equation is an identity, we can simplify both sides and see if they are equal. The right side of the equation can be rewritten using the commutative property of addition, which states that a + b = b + a for any numbers a and b . Therefore, 11.9 k + 11.21 = 11.21 + 11.9 k .
Comparing Both Sides Now we compare the left side and the right side of the equation:
Left side: 11.21 + 11.9 k Right side: 11.21 + 11.9 k
Since the left side is equal to the right side for all values of k , the equation is an identity.
Conclusion Therefore, the equation 11.21 + 11.9 k = 11.9 k + 11.21 is an identity.
Examples
In real life, identities are used in various fields such as physics and engineering to simplify equations and solve problems. For example, in circuit analysis, identities can be used to simplify complex expressions involving voltage, current, and resistance. By recognizing and applying identities, engineers can more easily analyze and design circuits.
The equation 11.21 + 11.9 k = 11.9 k + 11.21 is an identity because it is true for all values of k , as proven by the commutative property of addition. Thus, the answer is yes .
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