Solve for x: 9⋅x + 3 = 6⋅x - 3

To solve the equation ( 9 \cdot x + 3 = 6 \cdot x - 3 ), start by isolating the variable ( x ). First, you can bring all terms involving ( x ) to one side of the equation and constant terms to the other.

1. Subtract ( 6 \cdot x ) from both sides:

[

9 \cdot x - 6 \cdot x + 3 = -3

]

This simplifies to:

[

3 \cdot x + 3 = -3

]

2. Next, isolate ( 3 \cdot x ) by subtracting 3 from both sides:

[

3 \cdot x = -3 - 3

]

Which simplifies to:

[

3 \cdot x = -6

]

3. Finally, divide both sides by 3 to solve for ( x ):

[

x = \frac{-6}{3} = -2

]

Thus, the solution ( x = -2 ) correctly resolves the original equation. This