Problem 24 - Introductory Algebra for College Students

Question

Use an associative property to rewrite each algebraic expression. Once the grouping has been changed, simplify the resulting algebraic expression. $$9+(3+x)$$

Step-by-Step Solution

Answer

The simplified form of the given algebraic expression using the associative property is \(12 + x\).

Step 1: Understanding the Associative Property

In simple terms, the associative property is a property of some binary operations. In algebra, the rule is simply that you can add or multiply regardless of how the numbers are grouped. By 'grouped' we mean 'how you use parentheses'.

Step 2: Applying the Associative Property

For the given expression \(9+(3+x)\), the associative property allows us to change the grouping without changing the result. Hence, we can rewrite the expression as \((9+3)+x\).

Step 3: Simplifying the Resulting Expression

The resulting expression is \((9+3)+x\). This can be simplified further by adding 9 and 3 together to give \(12+x\).