206k views
0 votes
Instructions: Complete the following proof by dragging and dropping the correct reason into the space provided.

Given: −6a−5=−95

Instructions: Complete the following proof by dragging and dropping the correct reason-example-1

1 Answer

5 votes

Answer:

  • given
  • addition property of equality
  • division property of equality

Explanation:

The equation is solved by starting with the given equation, then performing inverse operations to undo what is done to the variable.

__

Step 1

The equation shown is the same as the given equation.

reason: given

Step 2

The equation shown has the "-5" term missing. That happens when +5 is added to both sides of the equation. -5 +5 = 0, and 0 added to anything leaves the value unchanged.

reason: addition property of equality

Step 3

The equation shown has the "-6" coefficient of 'a' missing. That happens when the equation is multiplied by the multiplicative inverse of -6. That is, it is divided by -6.

reason: division property of equality

_____

Additional comment

As we have noted in Step 3, division is the same as multiplication by the multiplicative inverse. The definition of multiplicative inverse tells you that the product of a number and its inverse is 1. The identity element property for multiplication tells you that multiplying by 1 leaves the value unchanged.

(1/(-6))(-6a) = 1a = a

So, the reason for Step 3 could also be "multiplication property of equality."

User Olympian
by
3.2k points