Problem 22 - Introductory Algebra for College Students

Question

Use the commutative property of multiplication to write an equivalent algebraic expression. $$6(x+4)$$

Step-by-Step Solution

Answer

The equivalent algebraic expression for \(6*(x+4)\) using the commutative property of multiplication is \(x*6 + 24\).

Step 1: Apply the distributive property

First, use the distributive property of multiplication over addition to simplify the expression. The distributive property states that for any real numbers a, b, and c, the equation a*(b+c) = a*b + a*c holds true. Applying this property to the expression 6*(x+4), we get a simplified expression of 6*x + 6*4.

Step 2: Solve the multiplication

Next, solve the multiplication in the simplified expression. This results in 6*x + 24.

Step 3: Reorder the expression

Last, use the commutative property of addition to reorder the terms in the expression. This property states that for any real numbers a and b, the equation a+b = b+a holds true. Using this property, we can rewrite the expression as x*6 + 24