Answer :
- Combine constant terms in the original expression: $6.2 + 8.7 = 14.9$, resulting in $8.9x + 14.9$.
- Compare each given expression to the simplified form $8.9x + 14.9$.
- Identify the equivalent expressions: $8.9x + 8.7 + 6.2$, $8.7 + 8.9x + 6.2$, and $6.2 + 8.7 + 8.9x$.
- The equivalent expressions are: $\boxed{8.9x + 8.7 + 6.2, 8.7 + 8.9x + 6.2, 6.2 + 8.7 + 8.9x}$.
### Explanation
1. Understanding the Problem
We are given the expression $8.9x + 6.2 + 8.7$ and asked to identify equivalent expressions from a list. To do this, we will simplify the given expression and compare it to the simplified forms of the expressions in the list.
2. Simplifying the Given Expression
First, let's simplify the given expression by combining the constant terms: $6.2 + 8.7 = 14.9$. So the given expression simplifies to $8.9x + 14.9$.
3. Comparing Expressions
Now, let's examine each of the expressions in the list and simplify them:
1. $9x + 6 + 9 = 9x + 15$. This is not equal to $8.9x + 14.9$.
2. $8.9 + 6.2 + 8.7x = 15.1 + 8.7x$. This is not equal to $8.9x + 14.9$.
3. $8.9x + 8.7 + 6.2 = 8.9x + 14.9$. This is equal to $8.9x + 14.9$.
4. $8.7 + 8.9x + 6.2 = 8.9x + 14.9$. This is equal to $8.9x + 14.9$.
5. $6.2 + 8.7 + 8.9 = 14.9 + 8.9 = 23.8$. This is not equal to $8.9x + 14.9$.
6. $6.2 + 8.7 + 8.9x = 14.9 + 8.9x = 8.9x + 14.9$. This is equal to $8.9x + 14.9$.
7. $8.9 + 6.2x + 8.7 = 17.6 + 6.2x$. This is not equal to $8.9x + 14.9$.
4. Identifying Equivalent Expressions
Therefore, the expressions equivalent to $8.9x + 6.2 + 8.7$ are:
* $8.9x + 8.7 + 6.2$
* $8.7 + 8.9x + 6.2$
* $6.2 + 8.7 + 8.9x$
5. Final Answer
The expressions equivalent to $8.9x + 6.2 + 8.7$ are $8.9x + 8.7 + 6.2$, $8.7 + 8.9x + 6.2$, and $6.2 + 8.7 + 8.9x$.
### Examples
Understanding equivalent expressions is crucial in many real-world scenarios. For instance, when calculating the total cost of items with a fixed price and variable quantities, recognizing equivalent expressions can simplify the calculation process. Imagine you're buying 'x' number of apples at $8.9 each, plus a fixed cost of $6.2 for a bag and $8.7 for delivery. Knowing that $8.9x + 6.2 + 8.7$ is the same as $8.9x + 14.9$ allows you to quickly determine the total cost by simply adding the fixed costs together. This skill is also useful in budgeting, financial planning, and even in scientific calculations where simplifying expressions can make complex problems easier to solve.
- Compare each given expression to the simplified form $8.9x + 14.9$.
- Identify the equivalent expressions: $8.9x + 8.7 + 6.2$, $8.7 + 8.9x + 6.2$, and $6.2 + 8.7 + 8.9x$.
- The equivalent expressions are: $\boxed{8.9x + 8.7 + 6.2, 8.7 + 8.9x + 6.2, 6.2 + 8.7 + 8.9x}$.
### Explanation
1. Understanding the Problem
We are given the expression $8.9x + 6.2 + 8.7$ and asked to identify equivalent expressions from a list. To do this, we will simplify the given expression and compare it to the simplified forms of the expressions in the list.
2. Simplifying the Given Expression
First, let's simplify the given expression by combining the constant terms: $6.2 + 8.7 = 14.9$. So the given expression simplifies to $8.9x + 14.9$.
3. Comparing Expressions
Now, let's examine each of the expressions in the list and simplify them:
1. $9x + 6 + 9 = 9x + 15$. This is not equal to $8.9x + 14.9$.
2. $8.9 + 6.2 + 8.7x = 15.1 + 8.7x$. This is not equal to $8.9x + 14.9$.
3. $8.9x + 8.7 + 6.2 = 8.9x + 14.9$. This is equal to $8.9x + 14.9$.
4. $8.7 + 8.9x + 6.2 = 8.9x + 14.9$. This is equal to $8.9x + 14.9$.
5. $6.2 + 8.7 + 8.9 = 14.9 + 8.9 = 23.8$. This is not equal to $8.9x + 14.9$.
6. $6.2 + 8.7 + 8.9x = 14.9 + 8.9x = 8.9x + 14.9$. This is equal to $8.9x + 14.9$.
7. $8.9 + 6.2x + 8.7 = 17.6 + 6.2x$. This is not equal to $8.9x + 14.9$.
4. Identifying Equivalent Expressions
Therefore, the expressions equivalent to $8.9x + 6.2 + 8.7$ are:
* $8.9x + 8.7 + 6.2$
* $8.7 + 8.9x + 6.2$
* $6.2 + 8.7 + 8.9x$
5. Final Answer
The expressions equivalent to $8.9x + 6.2 + 8.7$ are $8.9x + 8.7 + 6.2$, $8.7 + 8.9x + 6.2$, and $6.2 + 8.7 + 8.9x$.
### Examples
Understanding equivalent expressions is crucial in many real-world scenarios. For instance, when calculating the total cost of items with a fixed price and variable quantities, recognizing equivalent expressions can simplify the calculation process. Imagine you're buying 'x' number of apples at $8.9 each, plus a fixed cost of $6.2 for a bag and $8.7 for delivery. Knowing that $8.9x + 6.2 + 8.7$ is the same as $8.9x + 14.9$ allows you to quickly determine the total cost by simply adding the fixed costs together. This skill is also useful in budgeting, financial planning, and even in scientific calculations where simplifying expressions can make complex problems easier to solve.
