Proof: Algebra 3

Let's prove the following theorem:

if the following are true:
  • x = 12
  • d = (x ⋅ 2) + 1

then d = 25

Proof:

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Given
1 x = 12
2 d = (x ⋅ 2) + 1
Proof Table
# Claim Reason
1 x ⋅ 2 = 12 ⋅ 2 if x = 12, then x ⋅ 2 = 12 ⋅ 2
2 (x ⋅ 2) + 1 = (12 ⋅ 2) + 1 if x ⋅ 2 = 12 ⋅ 2, then (x ⋅ 2) + 1 = (12 ⋅ 2) + 1
3 d = (12 ⋅ 2) + 1 if d = (x ⋅ 2) + 1 and (x ⋅ 2) + 1 = (12 ⋅ 2) + 1, then d = (12 ⋅ 2) + 1
4 (12 ⋅ 2) + 1 = 25 (12 ⋅ 2) + 1 = 25
5 d = 25 if d = (12 ⋅ 2) + 1 and (12 ⋅ 2) + 1 = 25, then d = 25

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