Solve Linear Equation: (x-4)×3 = 2(x+6) Step-by-Step

To solve the equation $(x-4)\cdot3=2(x+6)$, we'll follow a systematic approach:

Step 1: Apply the distributive property to both sides of the equation.

• On the left side: $3(x-4) = 3x - 12$
• On the right side: $2(x+6) = 2x + 12$

Step 2: Rewrite the equation with the expanded terms:
$3x - 12 = 2x + 12$

Step 3: Move all terms involving $x$ to one side and constant terms to the other.

• Subtract $2x$ from both sides to move $x$ terms to the left:
  $3x - 2x = 12 + 12$ which simplifies to $x - 12 = 12$.
• Add 12 to both sides to isolate $x$:
  $x = 24$.

Therefore, the solution to the equation is $x = 24$.