1) 15 + 7n - 8 + 3n = 7n + 3n + 15 - 8 = (7 + 3)n + 15 - 8 = 10 n + 7
Associative Property of Addition
2) 12n + 2 (4 n + 2) = 12 n + 8 n + 4 = (12 + 8) n + 9 = 20 n + 9
Distributive Property of Equality
3) 15 n + (17 n + 9) = (15 n + 7 n) + 9 = (15 + 7) n + 9 = 22 n + 9
Addition Property of Equality,
4) 12 n + 6 + 7 n = 12 n + 7 n + 6 = (12 + 7) n + 6 = 19 n + 16
Associative Property of Addition
An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
We have,
The property used is the Associative Property of Addition, which allows us to regroup the terms without changing their order.
1. We grouped the terms (7n + 3n) and (15 - 8) together as (7 + 3)n and simplified them to get 10n + 7.
2. The property used is the Distributive Property of Multiplication over Addition, which allows us to distribute a factor to each term inside a parenthesis.
We distributed 2 to (4n + 2) to get 8n + 4, and then combined like terms to get,
12n + 8n + 4 = 20n + 4.
3. The property used is the Addition Property of Equality, which allows us to add the same quantity to both sides of an equation without changing its value.
We added 9 to both sides of the equation to get 15n + (17n + 9) + 9 = 15n + 17n + 18, which simplifies to 22n + 9.
4. The property used is the Associative Property of Addition, which allows us to regroup the terms without changing their order.
We grouped the terms (12n + 7n) and (6) together as (12 + 7)n and (6), and simplified to get 19n + 6.
Question:
Juan used algebraic properties to make an equivalent expression. He listed the properties in the order that he used them.
Step Property Used
1. Associative, 2. Distributive, 3. Addition
Which steps match the properties used?
15 + 7 n - 8 + 3n = 7 n + 3 n + 15 - 8 = (7 + 3) n + 15 - 8 = 10 n + 7
12 n + 2 (4 n + 2) = 12 n + 8 n + 4 = (12 + 8) n + 9 = 20 n + 9
15 n + (17 n + 9) = (15 n + 7 n) + 9 = (15 + 7) n + 9 = 22 n + 9
12 n + 6 + 7 n = 12 n + 7 n + 6 = (12 + 7) n + 6 = 19 n + 16