Question

use properties to rewrite the given equation. which equations have the same solution as 2.3p - 10.1 = 6.5p - 4 - 0.01p? select two options.
□ 2.3p - 10.1 = 6.4p - 4
□ 2.3p - 10.1 = 6.49p - 4
□ 230p - 1010 = 650p - 400 - p
□ 23p - 101 = 65p - 40 - p
□ 2.3p - 14.1 = 6.4p - 4

Explanation:

Step1: Simplify the right - hand side of the original equation

The original equation is \(2.3p - 10.1=6.5p - 4-0.01p\). Combine like terms on the right - hand side. We know that \(6.5p-0.01p=(6.5 - 0.01)p = 6.49p\). So the equation becomes \(2.3p-10.1 = 6.49p-4\). This means the second option is equivalent to the original equation.

Step2: Multiply the original equation by 100

Multiply each term in the original equation \(2.3p - 10.1=6.5p - 4-0.01p\) by 100. Using the distributive property \(a(b + c)=ab+ac\), we have:
\(100\times(2.3p)-100\times(10.1)=100\times(6.5p)-100\times4 - 100\times(0.01p)\)
\(230p-1010 = 650p-400 - p\)
This means the third option is equivalent to the original equation.

Step3: Analyze the first option

The first option is \(2.3p - 10.1=6.4p-4\). But we know that \(6.5p-0.01p = 6.49p
eq6.4p\), so this option is incorrect.

Step4: Analyze the fourth option

The fourth option is \(23p - 101=65p-40 - p\). If we multiply the original equation by 10, we get \(10\times(2.3p)-10\times(10.1)=10\times(6.5p)-10\times4-10\times(0.01p)\), which is \(23p - 101=65p-40-0.1p
eq65p - 40 - p\), so this option is incorrect.

Step5: Analyze the fifth option

The fifth option is \(2.3p-14.1 = 6.4p-4\). The left - hand side of the original equation is \(2.3p - 10.1\), and \(2.3p-10.1
eq2.3p - 14.1\), so this option is incorrect.

Answer:

B. \(2.3p - 10.1=6.49p - 4\)
C. \(230p - 1010=650p - 400 - p\)