Math  /  Algebra

QuestionHow can properties of operations help to generate equivalent expressions that can be used in solving problems?

Studdy Solution
Apply these properties to solve a sample problem:
Problem: Simplify the expression 2(x+3)+4x 2(x + 3) + 4x .
- Use the Distributive Property: 2(x+3)=2x+6 2(x + 3) = 2x + 6 .
- Substitute back into the expression: 2x+6+4x 2x + 6 + 4x .
- Use the Commutative Property to rearrange: 2x+4x+6 2x + 4x + 6 .
- Use the Associative Property to group like terms: (2x+4x)+6 (2x + 4x) + 6 .
- Simplify by combining like terms: 6x+6 6x + 6 .
The simplified expression is 6x+6 6x + 6 .
The properties of operations help generate equivalent expressions by allowing us to rearrange, regroup, expand, factor, and simplify expressions, which are essential steps in solving mathematical problems.

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