Question

which expression is equivalent to \\(\frac{4}{3}(9x - 2) - 3x\\)? \\(\bigcirc\\ 35x - 8\\) \\(\bigcirc\\ -33x - 8\\) \\(\bigcirc\\ -9x - \frac{8}{3}\\) \\(\bigcirc\\ 9x - \frac{8}{3}\\)

Explanation:

Step1: Distribute the fraction

First, distribute $\frac{4}{3}$ to the terms inside the parentheses: $\frac{4}{3}(9x - 2)=\frac{4}{3}\times9x-\frac{4}{3}\times2 = 12x-\frac{8}{3}$.

Step2: Subtract \(3x\)

Now, subtract \(3x\) from the result: \(12x-\frac{8}{3}-3x\).

Step3: Combine like terms

Combine the \(x\)-terms: \(12x - 3x=9x\), so the expression becomes \(9x-\frac{8}{3}\).

Answer:

\(9x - \frac{8}{3}\) (corresponding to the option with this expression)