Math Problem Statement
Identify the property that justifies each step asked about in the answer area below.
Line 1: , left parenthesis, 10, x, plus, 3, right parenthesis, plus, 4, x
Line 1: =
(10x+3)+4x
Line 2: , left parenthesis, 3, plus, 10, x, right parenthesis, plus, 4, x
Line 2: =
(3+10x)+4x
Line 3: , 3, plus, left parenthesis, 10, x, plus, 4, x, right parenthesis
Line 3: =
3+(10x+4x)
Line 4: , 3, plus, 14, x
Line 4: =
3+14x
Solution
Let's identify the property that justifies each step:
Line 1 to Line 2:
- Original Expression:
- Changed to:
Property Used: Commutative Property of Addition
- The commutative property of addition allows us to change the order of terms being added. Here, and were swapped in order.
Line 2 to Line 3:
- Original Expression:
- Changed to:
Property Used: Associative Property of Addition
- The associative property of addition allows us to regroup terms without changing their order. Here, the grouping was changed to combine and together.
Line 3 to Line 4:
- Original Expression:
- Changed to:
Property Used: Simplification or Addition
- This step simplifies the expression by adding the like terms and to get .
Would you like any further explanations or have any questions? Here are some related questions:
- Can the commutative property be applied to multiplication as well?
- What is the difference between commutative and associative properties in terms of their application?
- How can you identify like terms in an algebraic expression?
- Why is it important to combine like terms when simplifying expressions?
- How does the distributive property differ from the associative and commutative properties?
Tip: Practice identifying properties in various algebraic expressions to solidify your understanding and improve your problem-solving skills.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Properties of Addition
Formulas
-
Theorems
-
Suitable Grade Level
Grades 7-9
Related Recommendation
Identifying Properties of Addition in Algebraic Expressions
Understanding Properties of Addition in Algebraic Expressions
Identify Properties in Algebraic Transformations
Understanding Algebraic Properties: Commutative and Associative Properties in Algebraic Expressions
Identify the Commutative Property of Addition in Algebraic Expressions