use properties to rewrite the given equation. which equations have the same solution as 2.3p - 10.1 = 6.5p…

Explanation:

Step1: Simplify the original equation

First, simplify the right - hand side of the equation $2.3p−10.1 = 6.5p−4−0.01p$. Combine like terms: $6.5p−0.01p=6.49p$, so the original equation becomes $2.3p−10.1 = 6.49p−4$.

Step2: Analyze each option

Option 1: $2.3p−10.1 = 6.4p−4$

The right - hand side is different from the simplified original equation, so it does not have the same solution.

Option 2: $2.3p−10.1 = 6.49p−4$

This is the same as the simplified original equation, so it has the same solution.

Option 3: $230p−1010 = 650p−400−p$

Starting from the original equation $2.3p−10.1 = 6.49p−4$, multiply each term by 100. We get $2.3p\times100−10.1\times100=(6.49p - 4)\times100$, which simplifies to $230p−1010 = 649p−400$. And $650p−400−p=649p−400$, so this equation has the same solution.

Option 4: $23p−101 = 65p−40−p$

Multiply the original equation $2.3p−10.1 = 6.49p−4$ by 10. We get $23p−101 = 64.9p−40$. And $65p−40−p = 64p−40$, so it does not have the same solution.

Option 5: $2.3p−14.1 = 6.4p−4$

This is different from the simplified original equation, so it does not have the same solution.

Answer:

B. $2.3p−10.1 = 6.49p−4$, C. $230p−1010 = 650p−400−p$