Solve for x: 4⋅x + 9 = 8⋅x - 9.

To solve the equation (4 \cdot x + 9 = 8 \cdot x - 9), you can start by rearranging the equation to isolate the variable (x).

First, move all terms involving (x) to one side of the equation and constant terms to the other side. Subtract (4 \cdot x) from both sides:

[9 = 8 \cdot x - 4 \cdot x - 9.]

This simplifies to:

[9 + 9 = 4 \cdot x.]

[18 = 4 \cdot x.]

Now, to isolate (x), divide both sides by 4:

[x = \frac{18}{4}.]

Simplifying (\frac{18}{4}) results in:

[x = 4.5.]

Thus, the value of (x) that satisfies the equation is indeed 4.5. This answer is correct as it accurately follows the steps to isolate the variable and solves the equation successfully.