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Chapter 1: Problem 24

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

Short Answer

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

Step by step solution

01

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'.
02

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 \((9+3)+x\).
03

Simplifying the Resulting Expression

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

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Most popular questions from this chapter

Explain how to find the terms of the algebraic expression \(5 x-2 y-7\).

Determine whether 2 is a solution of \(13 x+3=3(5 x-1)\) (Section \(1.1,\) Example 4 )

Perform the indicated subtraction. $$-45-(-45)$$

Perform the indicated subtraction. $$-\frac{4}{9}-\left(-\frac{1}{9}\right)$$

Perform the indicated subtraction. $$5.7-3.3$$
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