When solving linear equations, the distributive property is a helpful tool. It allows us to multiply a single term by each term inside a set of parentheses. For our problem, we start with: \[ 4x - 2(3x + 7) = 6 + 5(x - 3) \] To distribute, multiply \(-2\) by each term inside its parentheses \((3x and 7)\), and do the same for \(5\) on the right side:
- \(-2 * 3x = -6x\)
- \(-2 * 7 = -14\)
- \(5 * x = 5x\)
- \(5 * -3 = -15\)
So, the equation becomes: \[ 4x - 6x - 14 = 6 + 5x - 15 \] This property helps simplify complex expressions, making the solving process smoother.