Question

The difference of 6 × a number and 5 is equal to 4 × that number. Which of the following equations shows the correct way to apply the Commutative Property of Multiplication?

a. 6(x - 5) = 4x
b. 4(x - 5) = 6x
c. 6(x + 5) = 4x
d. 4(x + 5) = 6x

Answer 1

The correct equation that applies the Commutative Property of Multiplication is 4(x + 5) = 6x.

Step-by-step explanation:

The correct equation that applies the Commutative Property of Multiplication in this scenario is d. 4(x + 5) = 6x.

The Commutative Property of Multiplication states that the order of factors in a multiplication operation can be changed without changing the result. In this equation, the number is being multiplied by a variable and a constant. By rearranging the expression, we can see that the order of multiplication is changed, but the result remains the same.

Let's break it down step by step:

1. The original equation is: 6 × a number - 5 = 4 × that number
2. Rewrite the equation in a way that the variable is on the left side and everything else is on the right side: 6 × a number = 4 × that number + 5
3. Apply the Commutative Property of Multiplication to rearrange the expression: 4 × that number + 5 = 6 × a number
4. Finally, rewrite the equation with the variable on the left side: 4(x + 5) = 6x