Let's simplify the expression step by step:

We start with the expression:

$\frac{3}{4}(8x - 3) - 2x$

Step 1: Distribute the $\frac{3}{4}$ to both terms inside the parentheses

$\frac{3}{4}(8x) - \frac{3}{4}(3)$

This becomes:

$\frac{3 \times 8x}{4} - \frac{3 \times 3}{4}$

Simplifying:

$\frac{24x}{4} - \frac{9}{4}$

Which simplifies to:

$6x - \frac{9}{4}$

Step 2: Subtract $2x$

Now we have:

$6x - \frac{9}{4} - 2x$

Combine like terms:

$(6x - 2x) - \frac{9}{4}$

Simplifying the $x$ terms:

$4x - \frac{9}{4}$

So, the simplified equivalent expression is:

$4x - \frac{9}{4}$

Conclusion:

The equivalent expression to $\frac{3}{4}(8x - 3) - 2x$ is:

$4x - \frac{9}{4}$

Would you like more details on any of the steps, or do you have any questions?

Here are some related questions:

1. How do you distribute constants over parentheses in algebraic expressions?
2. What does it mean to combine like terms in an expression?
3. How can I simplify expressions that involve fractions?
4. What is the importance of factoring in simplifying expressions?
5. How do you handle variables when simplifying algebraic expressions?

Tip: Always simplify terms with fractions and variables separately before combining them to avoid mistakes.