To eliminate fractions from the equation \( \frac{2}{3}x - 2 = \frac{3}{4} \), we can find a common multiple of the denominators 3 and 4. The least common multiple of 3 and 4 is 12.
Now, we will multiply the entire equation by 12 to eliminate the fractions:
\[ 12 \left(\frac{2}{3}x - 2\right) = 12 \left(\frac{3}{4}\right) \]
Distributing 12 gives:
\[ 12 \cdot \frac{2}{3}x - 12 \cdot 2 = 12 \cdot \frac{3}{4} \]
Calculating each term:
\[ 4 \cdot 2x - 24 = 9 \]
This simplifies to:
\[ 8x - 24 = 9 \]
Next, we can add 24 to both sides:
\[ 8x = 33 \]
Finally, divide by 8:
\[ x = \frac{33}{8} \]
Thus, when multiplying \( x \) by 5:
\[ x \cdot 5 = \frac{33}{8} \cdot 5 = \frac{165}{8} \]
So the final answer is:
\[ x \cdot 5 = \frac{165}{8} \]