Let's examine Vinay's steps and see where he might have gone wrong.
### Original Equation
The original equation is:
[tex]\[
-5(m - 2) = 25
\][/tex]
### Step 1: Apply the Distributive Property
The distributive property states that [tex]\( a(b + c) = ab + ac \)[/tex]. So we need to distribute the [tex]\(-5\)[/tex] to both terms inside the parentheses:
[tex]\[
-5(m - 2) = -5 \cdot m + (-5) \cdot (-2)
\][/tex]
Simplifying this, we get:
[tex]\[
-5m + 10
\][/tex]
So, the left-hand side of the equation becomes:
[tex]\[
-5m + 10
\][/tex]
### Step 2: Equate to the Right-Hand Side
After distribution, the equation should still be balanced, equated to the original right-hand side, which is 25:
[tex]\[
-5m + 10 = 25
\][/tex]
### Vinay's Equation
However, Vinay's resulting equation is:
[tex]\[
-5m + 10 = -125
\][/tex]
### Comparing Both Equations
The correct resulting equation from our steps is:
[tex]\[
-5m + 10 = 25
\][/tex]
While Vinay's equation is:
[tex]\[
-5m + 10 = -125
\][/tex]
Clearly, Vinay's resulting equation does not match the correct equation. Therefore, he made a mistake in his work.
### Identifying the Mistake
It looks like Vinay might have tried to multiply the right-hand side of the equation by -5 as well, which is incorrect. The distributive property only applies to the left-hand side within the parentheses, and not to the external result on the right-hand side.
### Conclusion
So, the correct answer is:
[tex]\[
\text{No, Vinay did not apply the distributive property correctly. He incorrectly transformed the right-hand side of the equation.}
\][/tex]
The correct application of the distributive property leads to the equation:
[tex]\[
-5m + 10 = 25
\][/tex]
