Solve for x: 3⋅x + 3 = 9⋅x - 3.

To solve the equation (3 \cdot x + 3 = 9 \cdot x - 3), we start by isolating the variable (x).

First, rearranging the equation helps simplify the terms. Subtract (3 \cdot x) from both sides:

[

3 + 3 \cdot x - 3 \cdot x = 9 \cdot x - 3 \cdot x - 3

]

This simplifies to:

[

3 = 6 \cdot x - 3

]

Next, add 3 to both sides:

[

3 + 3 = 6 \cdot x

]

This results in:

[

6 = 6 \cdot x

]

Now, divide both sides by 6:

[

x = 1

]

Thus, the solution to the equation is (x = 1).

This value satisfies the original equation. Substituting (x = 1) back into the original equation confirms the solution:

[

3 \cdot 1 + 3 = 9 \cdot 1 - 3

]

This simplifies to:

[