Question

What is the reason for each step in the solution of the equation?

4x−1=−2(x+1)

Drag and drop the reasons into the boxes to correctly complete the table.



4x−1=−2(x+1)

4x−1=−2x−2

6x−1=−2

6x=−1

x=−16


Distributive Property
Multiplication or Division Property of Equality
Commutative Property
Given
Addition or Subtraction Property of Equality

Answer 1

4x − 1 = −2 (x + 1) ⇒ Given

4x−1=−2x−2⇒ Distributive property (since we've multiplied out -2(x+1))

6x−1=−2 ⇒ Addition or Subtraction Property of Equality (We've added 2x onto the 4x to get 6x)

6x=−1 ⇒ Commutative Property (We've moved -1 to the other side to get the sum -2+1 = -1)

x=−¹/₆ ⇒ Multiplication or Division Property of Equality (We divided both sides by 6)

Answer 2

Answer:

Given

Distributive property

Addition or Subtraction Property of Equality

Addition or Subtraction Property of Equality

Multiplication or Division Property of Equality

Step-by-step explanation:

4x − 1 = −2 (x + 1)    Given   This is the starting point.

4x−1=−2x−2   Distributive property Distributes the -2 to the (x+1)

6x−1=−2   Addition or Subtraction Property of Equality  Adds 2x to both sides

6x=−1   Addition or Subtraction Property of Equality  Adds 1 to both sides

x=−¹/₆    Multiplication or Division Property of Equality  Divides both sides by 6