Is this equation an identity?
$-3(t+4)=-3 t-12$
Answer choices:
yes
no
Answer (2)
Expand the left side of the equation: − 3 ( t + 4 ) = − 3 t − 12 .
Compare the simplified left side with the right side: − 3 t − 12 = − 3 t − 12 .
Since both sides are equal, the equation is an identity.
The equation is an identity: yes .
Explanation
Analyzing the Equation We are given the equation − 3 ( t + 4 ) = − 3 t − 12 and asked to determine if it is an identity. An identity is an equation that is true for all values of the variable t . To check if the given equation is an identity, we will simplify the left side of the equation and compare it to the right side.
Expanding the Left Side We start by expanding the left side of the equation using the distributive property: − 3 ( t + 4 ) = − 3 \t − 3 × 4 = − 3 t − 12
Comparing Both Sides Now we compare the simplified left side, − 3 t − 12 , to the right side of the original equation, which is also − 3 t − 12 . Since both sides are equal, the equation is an identity.
Conclusion Therefore, the equation − 3 ( t + 4 ) = − 3 t − 12 is an identity because it is true for all values of t .
Examples
In real life, identities are useful in simplifying complex expressions in various fields such as physics and engineering. For example, when designing a circuit, engineers might use identities to simplify the equations describing the circuit's behavior, making it easier to analyze and optimize the design. Similarly, in physics, identities can be used to simplify equations of motion or energy conservation, leading to more efficient calculations and a better understanding of the underlying principles. Understanding identities helps in simplifying problems and finding equivalent representations, which is a fundamental skill in many quantitative disciplines.
The equation − 3 ( t + 4 ) = − 3 t − 12 is an identity because both sides simplify to the same expression, − 3 t − 12 , which is true for all values of t . The correct answer is: yes.
;
