x + 1 + 1 + 6x > 3(x − 4) − (x − 4

Sure, let's solve this inequality step by step:

1. First, simplify the left side of the inequality: x + 1 + 1 + 6x = 7x + 2
2. Then, simplify the right side of the inequality: 3(x - 4) - (x - 4) = 3x - 12 - x + 4 = 2x - 8
3. Now, set the simplified expressions against each other: 7x + 2 > 2x - 8
4. To isolate x, subtract 2x from both sides: 7x - 2x > 2x - 2x - 8, which simplifies to 5x + 2 > -8
5. Then, subtract 2 from both sides: 5x > -8 - 2, which simplifies to 5x > -10
6. Finally, divide both sides by 5 to solve for x: x > -10/5, which simplifies to x > -2

So, the solution to the inequality is x > -2.