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

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

Step2: Check Other Options (Optional)

• For Option B: \(\frac{2}{3}(2x + 3)=\frac{2}{3}\times2x+\frac{2}{3}\times3=\frac{4}{3}x+2

eq\frac{2}{3}x + 1\)

• For Option C: \(\frac{2}{3}(3x + 2)=\frac{2}{3}\times3x+\frac{2}{3}\times2 = 2x+\frac{4}{3}

eq\frac{2}{3}x + 1\)

• For Option D: \(\frac{2}{3}(3x + 1)=\frac{2}{3}\times3x+\frac{2}{3}\times1=2x+\frac{2}{3}

eq\frac{2}{3}x + 1\)

Answer:

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