You should evaluate with numbers other than 0, because sometimes using x = 0 will give a _ equivalency.

Question

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: $$\frac{7.037}{3.1}\approx 2.27\text{and}\frac{1.798}{3.1}\approx 0.58$$

Thus: $$E_2\approx 2.27-0.58x$$

Now, notice that both expressions simplify to the same form: $$E_1=-0.58x+2.27\text{and}{E}_2\approx -0.58x+2.27$$

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 $\frac{7.037-2.798x}{3.1}$