Let's solve the equation $\frac{2}{3}(4x - 3) = 14$.

Step 1: Eliminate the fraction

To eliminate the fraction, multiply both sides of the equation by 3:

$3 \times \frac{2}{3}(4x - 3) = 3 \times 14$

This simplifies to:

$2(4x - 3) = 42$

Step 2: Distribute the 2

Distribute the 2 on the left-hand side:

$8x - 6 = 42$

Step 3: Isolate the variable term

Add 6 to both sides of the equation:

$8x = 48$

Step 4: Solve for $x$

Divide both sides by 8:

$x = 6$

Final Answer:

$x = 6$

Would you like more details or further explanations?

Here are 5 related questions to consider:

1. How do you solve linear equations with fractions?
2. How can you check the solution to this equation?
3. What happens if you distribute before eliminating the fraction?
4. How do you solve equations involving multiple variables?
5. How can linear equations be used in real-world problems?

Tip: When working with equations that involve fractions, it's often easier to eliminate the fraction early on by multiplying both sides of the equation by the denominator.