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

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.\n□ 2.3p - 10.1 = 6.4p - 4\n□ 2.3p - 10.1 = 6.49p - 4\n□ 230p - 1010 = 650p - 400 - p\n□ 23p - 101 = 65p - 40 - p\n□ 2.3p - 14.1 = 6.4p - 4

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.\n□ 2.3p - 10.1 = 6.4p - 4\n□ 2.3p - 10.1 = 6.49p - 4\n□ 230p - 1010 = 650p - 400 - p\n□ 23p - 101 = 65p - 40 - p\n□ 2.3p - 14.1 = 6.4p - 4

Answer

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 is (2.3p−10.1 = 6.49p−4).

Step2: Check each option

  • Option 1: (2.3p−10.1 = 6.4p−4), the coefficient of (p) on the right - hand side is different from the simplified original equation, so it has a different 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: Multiply the original equation (2.3p−10.1 = 6.49p−4) by 100. We get (230p−1010 = 649p−400). The given equation (230p−1010 = 650p−400 - p=649p−400), so it has the same solution.
  • Option 4: Multiply the original equation (2.3p−10.1 = 6.49p−4) by 10. We get (23p−101 = 64.9p−40), not (23p−101 = 65p−40 - p), so it has a different solution.
  • Option 5: The left - hand side of (2.3p−14.1 = 6.4p−4) is different from the original equation, so it has a different solution.

Answer:

  1. (2.3p−10.1 = 6.49p−4)
  2. (230p−1010 = 650p−400 - p)