Question

Please help!

The table below shows an expression that has been simplified. Fill in the property used to justify each step of simplification:

Steps: Properties:
3 + 4(x + 1) Given
3 + (4x + 4) 1.
(4x + 4) + 3 2.
4x + (4 + 3) 3.
4x + 7 4.

Answer 1

1. Distributive property: Distributing the factor 4 into (x+1).
2. Property of addition: Moving around the expression so that the variable is upfront. (When adding this doesn't matter).
3. Property of separation: Moving around the parenthesis (since all numbers have positive signs, this doesn't alter anything).
4. PEMDAS property: Solving the parenthesis first and writing the resulting simplified answer.

Answer 2

Thank you @naranjja !

What about this one?

Steps Properties
k+(k+2) Given
(k+k)+2
(1k+1k)+2
(1+1)k+2
2k+2

Answer 3

No problem!

1. Property of separation: Moving around the parenthesis (since all numbers have positive signs, this doesn't alter anything).
2. Property of coefficients: 1 is coefficient that is unnecessary to write. Writing it makes no difference.
3. Factorizing property: The k is separated from the addition as a factor to (1+1)
4. PEMDAS property: Solving the parenthesis and using its result as the new coefficient for k.