To rewrite the equation \( \frac{2}{3}x - 2 = \frac{3}{4} \) without fractions, we can first find a common denominator for all the terms in the equation. The common denominator for 3 and 4 is 12.
We can multiply the entire equation by 12 to eliminate the fractions:
\[ 12 \left(\frac{2}{3}x\right) - 12(2) = 12\left(\frac{3}{4}\right) \]
Now, simplifying each term:
\[ 12 \cdot \frac{2}{3}x = 8x \quad \text{(since } 12 \div 3 = 4 \text{ and } 4 \cdot 2 = 8\text{)} \] \[ 12 \cdot (-2) = -24 \] \[ 12 \cdot \frac{3}{4} = 9 \quad \text{(since } 12 \div 4 = 3 \text{ and } 3 \cdot 3 = 9\text{)} \]
Putting it all together, we have:
\[ 8x - 24 = 9 \]
Next, we can solve for \( x \):
- Add 24 to both sides:
\[ 8x = 9 + 24 \] \[ 8x = 33 \]
- Finally, divide by 8:
\[ x = \frac{33}{8} \]
Thus, the final answer is:
\[ x = \frac{33}{8} \]