Question

which expression is equivalent to \\(\frac{2}{3}x + 1\\)?

a \\(\frac{1}{3}(2x + 3)\\)

b \\(\frac{2}{3}(2x + 3)\\)

c \\(\frac{2}{3}(3x + 2)\\)

d \\(\frac{2}{3}(3x + 1)\\)

Explanation:

Step1: Expand Option A

Expand $\frac{1}{3}(2x + 3)$ using the distributive property $a(b + c)=ab+ac$. So, $\frac{1}{3}\times2x+\frac{1}{3}\times3=\frac{2}{3}x + 1$.

Step2: Check Other Options (Optional)

• Option B: Expand $\frac{2}{3}(2x + 3)=\frac{4}{3}x + 2

eq\frac{2}{3}x + 1$.

• Option C: Expand $\frac{2}{3}(3x + 2)=2x+\frac{4}{3}

eq\frac{2}{3}x + 1$.

• Option D: Expand $\frac{2}{3}(3x + 1)=2x+\frac{2}{3}

eq\frac{2}{3}x + 1$.

Answer:

A. $\frac{1}{3}(2x + 3)$