To solve the equation, we will simplify and combine like terms on both sides of the equation.

Starting with the left side: 19x + 8 - 1(x + 4) = 4x + 12 - 2(4 - 7x)

Distribute the -1 and -2: 19x + 8 - x - 4 = 4x + 12 - 8 + 14x

Combine like terms: 18x + 4 = 18x + 4 + 14x + 4

Simplify: 18x + 4 = 32x + 8

Now, let’s solve for x: Subtract 18x from both sides: 4 = 14x + 8

Subtract 8 from both sides: -4 = 14x

Divide both sides by 14: -4/14 = x -2/7 = x

To verify the answer, substitute x = -2/7 back into the original equation: 19x + 8 - 1(x + 4) = 4x + 12 - 2(4 - 7x)

19(-2/7) + 8 - 1(-2/7 + 4) = 4(-2/7) + 12 - 2(4 - 7(-2/7))

Simplify: -38/7 + 8 - (-2/7 + 28/7) = -8/7 + 12 - 2(4 + 2)

-38/7 + 8 + 2/7 - 28/7 = -8/7 + 12 - 2(6)

Combine like terms: -38/7 + 8 + 2/7 - 28/7 = -8/7 + 12 - 12

-38/7 + 2/7 - 28/7 = -8/7

-64/7 = -8/7

The equation is true, so the solution x = -2/7 is verified.