Proof: Inequality Problem

Let's prove the following theorem:

if x + 4 > 9, then x > 5

The inequality properties allow us to add -4 to both sides.

x + 4 - 4 = x

and

9 - 4 = 5

so

x > 5

Proof:

View as a tree | View dependent proofs | Try proving it

Given
1 x + 4 > 9
Proof Table
# Claim Reason
1 (x + 4) + (4 ⋅ (-1)) > 9 + (4 ⋅ (-1)) if x + 4 > 9, then (x + 4) + (4 ⋅ (-1)) > 9 + (4 ⋅ (-1))
2 9 + (4 ⋅ (-1)) = 5 9 + (4 ⋅ (-1)) = 5
3 (x + 4) + (4 ⋅ (-1)) = x (x + 4) + (4 ⋅ (-1)) = x
4 x > 5 if 9 + (4 ⋅ (-1)) = 5 and (x + 4) + (4 ⋅ (-1)) = x and (x + 4) + (4 ⋅ (-1)) > 9 + (4 ⋅ (-1)), then x > 5

Comments

Please log in to add comments