Solve for X in -3x+8=7x-12: Linear Equation Solution

We will solve the equation step by step:

Given equation:
$-3x + 8 = 7x - 12$

• Step 1: Move all $x$-terms to one side by adding $3x$ to both sides.
  $-3x + 3x + 8 = 7x + 3x - 12$
  This simplifies to:
  $8 = 10x - 12$
• Step 2: Move constant terms to the opposite side by adding $12$ to both sides.
  $8 + 12 = 10x - 12 + 12$
  Which simplifies to:
  $20 = 10x$
• Step 3: Solve for $x$ by dividing both sides by $10$.
  $\frac{20}{10} = \frac{10x}{10}$
  This gives us:
  $x = 2$

Therefore, the solution to the equation is $x = 2$.