you assume the opposite of what you want to prove, and then show that this assumption leads to a contradiction or an absurdity. In this case, we want to prove that "if -3x + 4 < 7, then x > -1" indirectly.
Assume the opposite of what we want to prove, which is "if -3x + 4 < 7, then x ≤ -1".
Adding 3x to both sides of the inequality, we get:
4 < 3x + 7
Subtracting 7 from both sides, we get:
-3 < 3x
Dividing both sides by 3, we get:
-1 < x
This contradicts our assumption that x ≤ -1. Therefore, our assumption is false, and the original statement "if -3x + 4 < 7, then x > -1" is true. This completes the indirect proof.