To solve the linear equation 6x - 2(4x - 9) = 2(3 + 5x), we will simplify the equation and then solve for x.

First, distribute the -2 and 2 on both sides of the equation: 6x - 8x + 18 = 6 + 10x

Combine like terms: -2x + 18 = 6 + 10x

Next, move all the x terms to one side of the equation and the constant terms to the other side: -2x - 10x = 6 - 18

Combine like terms: -12x = -12

Divide both sides of the equation by -12 to solve for x: x = -12 / -12 x = 1

To verify the answer, substitute x = 1 back into the original equation: 6(1) - 2(4(1) - 9) = 2(3 + 5(1)) 6 - 2(4 - 9) = 2(3 + 5) 6 - 2(-5) = 2(8) 6 + 10 = 16 16 = 16

The equation is true when x = 1, so the solution is verified.