Question

You should evaluate with numbers other than 0, because sometimes using x = 0 will give a _ equivalency.
Equivalent Expressions
-0.58x + 2.27 and 7.037-1.798x / 3.1

_ Expressions
-0.58x + 2.27 and 7.037-2.798x / 3.1
If we evaluate the expressions, for x = 0, the values are equivalent.
If we substitute x = 1 we get 1.69 on the left and approximately 1.37 on the right.

Answer 1

To determine if the two expressions \(-0.58x + 2.27\) and \(\frac{7.037 - 1.798x}{3.1}\) are equivalent, we can set them equal to each other and analyze the results.

1. **The first expression** is:
\[
E_1 = -0.58x + 2.27
\]

2. **The second expression** is:
\[
E_2 = \frac{7.037 - 1.798x}{3.1}
\]

To simplify this, we can perform the division:
\[
E_2 = \frac{7.037}{3.1} - \frac{1.798x}{3.1}
\]
which gives us:
\[
E_2 \approx 2.27 - 0.58x
\]

Now, substituting the constants:
\[
\frac{7.037}{3.1} \approx 2.27 \quad \text{and} \quad \frac{1.798}{3.1} \approx 0.58
\]

Thus:
\[
E_2 \approx 2.27 - 0.58x
\]

Now, notice that both expressions simplify to the same form:
\[
E_1 = -0.58x + 2.27 \quad \text{and} \quad E_2 \approx -0.58x + 2.27
\]

If we plug in \(x = 0\) into both:
- For \(E_1\):
\[
E_1(0) = -0.58(0) + 2.27 = 2.27
\]

- For \(E_2\):
\[
E_2(0) = \frac{7.037 - 1.798(0)}{3.1} = \frac{7.037}{3.1} \approx 2.27
\]

This validates that the expressions are equivalent when \(x = 0\).

Next, evaluating for \(x = 1\):
- For \(E_1\):
\[
E_1(1) = -0.58(1) + 2.27 = -0.58 + 2.27 = 1.69
\]

- For \(E_2\):
\[
E_2(1) = \frac{7.037 - 1.798(1)}{3.1} = \frac{7.037 - 1.798}{3.1} = \frac{5.239}{3.1} \approx 1.69
\]

**Final Verification:**
Both expressions yield the same outcome of approximately \(1.69\) at \(x = 1\).

### Conclusion:
The expressions \(-0.58x + 2.27\) and \(\frac{7.037 - 1.798x}{3.1}\) are equivalent for all values of \(x\). However, the other expression you compared, \(-0.58x + 2.27\) and \(\frac{7.037 - 2.798x}{3.1}\), likely is not equivalent as it alters the coefficient of \(x\), thus changing the relationship captured in the expressions.

So the correct statement would be:
- **Equivalent Expressions**: \(-0.58x + 2.27\) and \(\frac{7.037 - 1.798x}{3.1}\)
- **Not Equivalent Expressions**: \(-0.58x + 2.27\) and \(\frac{7.037 - 2.798x}{3.1}\)