Which expression is equivalent to 2.8k – 8.4
The Correct Answer and Explanation is :
To simplify the expression (2.8k – 8.4), we can look for equivalent expressions and analyze their components. First, we can factor the expression. We notice that both terms share a common factor:
Step 1: Factoring Out the Common Factor
The terms (2.8k) and (-8.4) can be factored by noticing that (2.8) can be factored as (2.8) itself, and (-8.4) can be rewritten in terms of (2.8):
[
-8.4 = -3 \times 2.8
]
Thus, we can express the entire expression in terms of (2.8):
[
2.8k – 8.4 = 2.8k – 3 \times 2.8
]
Step 2: Factoring Out (2.8)
Now, we factor out (2.8) from both terms:
[
2.8(k – 3)
]
Conclusion
The simplified expression (2.8(k – 3)) is equivalent to the original expression (2.8k – 8.4).
Why This Works
Factoring is a powerful algebraic technique that allows us to simplify expressions and make them easier to manipulate. When we factor, we are essentially rewriting the expression in a different form, which can reveal properties about the equation or make it easier to solve for variables.
This technique is especially useful in solving equations or inequalities, as it can help identify the roots or points where the expression equals zero. For example, in our factored expression (2.8(k – 3)), we can see that the expression equals zero when (k = 3).
In summary, the expression (2.8k – 8.4) simplifies to (2.8(k – 3)), demonstrating the power of factoring to reveal the underlying structure of algebraic expressions. This approach not only aids in simplifying but also enhances our understanding of how different components relate to one another.