The image provides a problem asking to write an expression for the length of a rectangle. The area of the rectangle is given as $2x^2 - 6x$ square units, and the width is provided as $2x$ units. The formula for the area of a rectangle is:

$\text{Area} = \text{Length} \times \text{Width}$

We can rearrange this to solve for the length:

$\text{Length} = \frac{\text{Area}}{\text{Width}}$

Given the area is $2x^2 - 6x$ and the width is $2x$, the expression for the length is:

$\text{Length} = \frac{2x^2 - 6x}{2x}$

We can simplify this by factoring out the common terms:

$\text{Length} = \frac{2x(x - 3)}{2x}$

Canceling the $2x$ terms:

$\text{Length} = x - 3$

Thus, the expression for the length of the rectangle is $x - 3$.

Would you like further details or have any questions?

Here are 5 related questions for further practice:

1. What happens to the length if $x = 4$?
2. How would the expression for length change if the width was $3x$ instead?
3. Can the length ever be negative, and under what conditions?
4. How does the factorization of polynomials help in solving area-related problems?
5. What is the length when the area becomes a perfect square trinomial?

Tip: Always check if expressions can be simplified by factoring out common terms to make calculations easier.