Question

which expression is equivalent to \\(\frac{2}{3}(4x - 9)\\)?
a \\(\frac{8x - 18}{3}\\)
b \\(\frac{8x - 9}{3}\\)
c \\(\frac{8}{3}(x + 18)\\)
d \\(\frac{8}{3}(x - 12)\\)

Explanation:

Step1: Apply distributive property

To simplify \(\frac{2}{3}(4x - 9)\), we use the distributive property \(a(b - c)=ab - ac\). Here, \(a=\frac{2}{3}\), \(b = 4x\), and \(c=9\). So we multiply \(\frac{2}{3}\) with each term inside the parentheses:
\(\frac{2}{3}\times4x-\frac{2}{3}\times9\)

Step2: Calculate each term

For the first term, \(\frac{2}{3}\times4x=\frac{8x}{3}\) (since \(2\times4 = 8\)). For the second term, \(\frac{2}{3}\times9 = 6\) (because \(9\div3 = 3\) and \(3\times2 = 6\)), so the second term becomes \(- 6\). But we can also write the expression with a common denominator. Let's rewrite \(-6\) as \(\frac{-18}{3}\) (because \(6=\frac{18}{3}\)). So the expression \(\frac{8x}{3}-6\) can be written as \(\frac{8x}{3}-\frac{18}{3}\), and combining the numerators over the common denominator gives \(\frac{8x - 18}{3}\).

Answer:

A. \(\frac{8x - 18}{3}\)