The general approach to solving any such inequality is to get the variable by itself on one side of the relationship symbol. The instructions for this can vary, but here is a set of instructions that will always work.
1. Subtract the expression on the right side of the relationship symbol.
... 7x + 1 < 4(x - 2) . . . . starting inequality
... 7x +1 - 4(x -2) < 0 . . . after step 1
2. Eliminate parentheses and collect terms.
... 7x +1 -4x +8 < 0
... 3x +9 < 0 . . . . . . . . . after step 2
3. Divide by the coefficient of the variable. Here, divide by 3. If the coefficient of the variable is negative, also reverse the relationship symbol (≥ becomes ≤, for example).
... x + 3 < 0 . . . . . . . . . we divided by 3
4. Add the opposite of the constant, if any.
... x < -3 . . . . . . . . . . . . after adding -3
This solution matches your 4th selection:
... {x | x < -3}
