Which expression is equivalent to –4.5 – 6.2y?
The Correct Answer and Explanation is:
The expression (-4.5 – 6.2y) can be simplified or rewritten in equivalent forms using properties of algebra. However, it cannot be further simplified unless more context or specific operations (like factoring or substitution) are provided. But let’s break down the expression to understand its structure and explore equivalent expressions.
Step-by-Step Breakdown:
The given expression is:
[
-4.5 – 6.2y
]
- Identify the terms:
- (-4.5) is a constant term (a number without a variable).
- (-6.2y) is a term involving a variable (y), where (-6.2) is the coefficient of (y).
- Rearranging the expression:
The expression is linear in (y) and consists of two distinct terms. Rearranging the order of terms does not change the expression’s value. We can write it as: [
-6.2y – 4.5
] This is still equivalent to the original expression, simply written in a different order. - Factoring out a common factor (if applicable):
There is no common factor between (-4.5) and (-6.2y) that can be factored out in a meaningful way that would simplify the expression further. Therefore, factoring isn’t useful here. - Equivalent expressions:
An equivalent expression could involve manipulating the expression algebraically, such as by factoring, but since there is no common factor and no additional operations, the simplest equivalent form is the original expression itself or its rearranged form.
Conclusion:
The expression (-4.5 – 6.2y) is already in a simplified and standard form. Its rearranged form (-6.2y – 4.5) is also an equivalent expression, but it essentially represents the same mathematical relationship between the terms.
Therefore, the correct answer is:
[
-4.5 – 6.2y \quad \text{or} \quad -6.2y – 4.5
]
Both are equivalent expressions.