Question

The following pairs of equations are equivalent. Determine

the property that was used to write the second equation.
a. 2(x + 4) = 14 - 6x and 2x + 8 = 14 - 6x

Answer 1

The equations 2(x + 4) = 14 - 6x and 2x + 8 = 14 - 6x illustrate the use of the Distributive Property, where multiplication is distributed over addition within parentheses.

Step-by-step explanation:

The pairing of equations 2(x + 4) = 14 - 6x and 2x + 8 = 14 - 6x demonstrates the use of the Distributive Property. The Distributive Property allows us to multiply a single term and two or more terms inside a set of parentheses so that we end up with an equivalent expression. Here's how it works in the given example:

• Start with the original equation: 2(x + 4) = 14 - 6x.
• Apply the Distributive Property by multiplying 2 times each term inside the parentheses, 'x' and '4': 2 * x + 2 * 4.
• As a result, we get the equivalent equation: 2x + 8 = 14 - 6x.