Problem 21 - Introductory Algebra for College Students

Question

Use the commutative property of multiplication to write an equivalent algebraic expression. $$5(x+3)$$

Step-by-Step Solution

Answer

The equivalent algebraic expression using the commutative property of multiplication is \(5(x+3)\).

Step 1: Understanding the Commutative Property of Multiplication

The commutative property of multiplication tells us that changing the order of the factors does not change the product. In other words, if we are given the multiplication problem \(a \times b\), it is the same as \(b \times a\). The result would be the same.

Step 2: Applying the Commutative Property

To apply the Commutative Property of Multiplication to the given expression \(5(x+3)\), we should understand that it can be written equivalently as \((x+3)5\). This is possible as the commutative property allows for the order of factors to be changed.

Step 3: Simplifying the Expression

However, in algebra, it's common to put the numeric coefficient before the variable. Therefore, \((x+3)5\) can be rewritten in a more standard form as \(5(x+3)\).