Solve for \( x \): \( 3(x - 2) = 6 \).

To solve the equation ( 3(x - 2) = 6 ), start by isolating the term that contains ( x ). The first step is to eliminate the coefficient of ( x ) by dividing both sides of the equation by 3. This gives:

[

x - 2 = 2

]

Next, to isolate ( x ), add 2 to both sides:

[

x = 2 + 2

]

This simplifies to:

[

x = 4

]

Thus, the solution for ( x ) is 4. When substituting back into the original equation to verify, replacing ( x ) with 4 yields:

[

3(4 - 2) = 3 \times 2 = 6

]

Since both sides of the equation are equal, it confirms that ( x = 4 ) is indeed the correct solution.