Question - Solving for Expression with Given Values
Solution:
To solve the question, we need to find which expression equals $$ \frac{10}{3} $$ when $$ x = \frac{2}{3} $$.Let's start by evaluating each expression with $$ x = \frac{2}{3} $$:A) $$ 4x - 2 $$\[ 4\left(\frac{2}{3}\right) - 2 = \frac{8}{3} - 2 = \frac{8}{3} - \frac{6}{3} = \frac{2}{3} \]B) $$ 2 - 8x $$\[ 2 - 8\left(\frac{2}{3}\right) = 2 - \frac{16}{3} = \frac{6}{3} - \frac{16}{3} = -\frac{10}{3} \]C) $$ 8x - 6 $$\[ 8\left(\frac{2}{3}\right) - 6 = \frac{16}{3} - 6 = \frac{16}{3} - \frac{18}{3} = -\frac{2}{3} \]D) $$ 5x $$\[ 5\left(\frac{2}{3}\right) = \frac{10}{3} \]Option D, $$ 5x $$, gives us the correct value of $$ \frac{10}{3} $$ when $$ x = \frac{2}{3} $$. Therefore, the correct answer is D) $$ 5x = \frac{10}{3} $$.
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