Fill in the blanks!

Question

Is -0.58x + 2.27 equivalent to 7.037 - 1.798x / 3.1 ?
Use _ to evaluate the expressions.
Let x = 0.
_ = 2.27
The expressions are equivalent for 0.
In order to be equivalent, the expressions must be equal when _ value of x is used.
Let x = 10.

First expression:
-0.58(10) + 2.27
-5.8 + 2.27
-3.53

Second expression:
7.037 - 1.798(10) / 3.1
7.037 - 17.98 / 3.1
-10.943 / 3.1
_

We can conclude that these two expressions are _.

Answer 1

Let's fill in the blanks step by step based on the problem provided.

1. Based on the first sentence, we can conclude with: "Use _ to evaluate the expressions." Therefore, we'll put: x

2. The second sentence states: "Let x = 0." After evaluating the first expression at x = 0, we find that: 2.27 is correct.

3. The next sentence is: "The expressions are equivalent for 0." We can put: any

4. The sentence states: "In order to be equivalent, the expressions must be equal when _ value of x is used." We can insert: the given

5. For the evaluations: "Let x = 10." The first expression: -0.58(10) + 2.27 -5.8 + 2.27 -3.53

6. For the second expression: 7.037 - 1.798(10) / 3.1 We first calculate: 7.037 - 17.98 / 3.1 -17.98 / 3.1 gives approximately -5.8. Therefore: 7.037 - 5.8 gives: 1.237

7. The final sentence concludes: "We can conclude that these two expressions are _." Therefore, we can fill it with: not equivalent.

Putting it all together, we have:

Is -0.58x + 2.27 equivalent to 7.037 - 1.798x / 3.1 ?
Use x to evaluate the expressions.
Let x = 0.
2.27
The expressions are equivalent for 0.
In order to be equivalent, the expressions must be equal when the given value of x is used.
Let x = 10.
First expression:
-0.58(10) + 2.27
-5.8 + 2.27
-3.53
Second expression:
7.037 - 1.798(10) / 3.1
7.037 - 17.98 / 3.1
-17.98 / 3.1
1.237
We can conclude that these two expressions are not equivalent.

Answer 2

fill in all the blanks!

Answer 3

Sure! Here is the completed version with all the blanks filled in:

Is -0.58x + 2.27 equivalent to 7.037 - 1.798x / 3.1?
Use x to evaluate the expressions.
Let x = 0.
2.27
The expressions are equivalent for 0.
In order to be equivalent, the expressions must be equal when the same value of x is used.
Let x = 10.

First expression:
-0.58(10) + 2.27
-5.8 + 2.27
-3.53

Second expression:
(7.037 - 1.798(10)) / 3.1
(7.037 - 17.98) / 3.1
-10.943 / 3.1
-3.53

We can conclude that these two expressions are equivalent.

Overall, it looks like the first expression and the adjusted second expression do yield the same value when \( x = 10 \), confirming their equivalence!