2(x-5)+3x < 4(x-6)+1

2x - 10 + 3x < 4x - 24 + 1
5x - 4x < -23 + 10
x < -13

Thank you very much Reiny!

To solve this inequality, we need to simplify the expression and isolate the variable x on one side. Here's how you can do that step by step:

1. Distribute the terms inside the parentheses:
2(x-5) + 3x < 4(x-6) + 1
2x - 10 + 3x < 4x - 24 + 1

2. Combine like terms on both sides of the inequality:
2x + 3x - 10 < 4x - 23

3. Simplify further:
5x - 10 < 4x - 23

4. Move all terms containing x to one side and the constant terms to the other side. To do this, subtract 4x from both sides and add 10 to both sides:
5x - 4x < -23 + 10
x < -13

Therefore, the solution to the given inequality is x < -13.