Question

which expression is equivalent to \\(\frac{1}{5}(15 + 10x - 5)\\)? \\(\boldsymbol{\text{ⓐ}}\\) \\(2 + 2x\\) \\(\boldsymbol{\text{ⓑ}}\\) \\(2 - 2x\\) \\(\boldsymbol{\text{ⓒ}}\\) \\(-2 + 2x\\) \\(\boldsymbol{\text{ⓓ}}\\) \\(-2 - 2x\\)

Explanation:

Step1: Simplify the expression inside the parentheses

First, combine the constant terms inside the parentheses: \(15 - 5 + 10x = 10 + 10x\)

Step2: Distribute the \(\frac{1}{5}\)

Multiply each term inside the parentheses by \(\frac{1}{5}\): \(\frac{1}{5}(10 + 10x) = \frac{1}{5} \times 10 + \frac{1}{5} \times 10x\)
Calculate each product: \(\frac{10}{5} + \frac{10x}{5} = 2 + 2x\)

Answer:

A. \(2 + 2x\)