You're looking at a
two-column proof in algebra — where the left column lists
statements (mathematical steps), and the right column lists
reasons (why each step is valid).
The goal is to solve the equation:
>
45 + 2(x – 10) = 85
and prove that
x = 30
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Let’s go through each step logically, as shown in the image:
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Statement 1: 45 + 2(x – 10) = 85
✔ Reason: Given
This is the original equation provided in the problem. It’s the starting point.
---
Statement 2: 2(x – 10) = 40
✔ Reason: Subtraction Property of Equality
To isolate the term with x, we subtract 45 from
both sides of the equation:
> 45 + 2(x – 10) – 45 = 85 – 45
→ 2(x – 10) = 40
*(Note: The handwritten reason says “Subtraction Prop.” — this is short for “Subtraction Property of Equality”)*
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Statement 3: 2x – 20 = 40
✔ Reason: Distributive Property
Apply the distributive property to expand 2(x – 10):
> 2·x – 2·10 = 2x – 20
So now the equation becomes:
> 2x – 20 = 40
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Statement 4: 2x = 60
✔ Reason: Addition Property of Equality
Add 20 to both sides to isolate the term with x:
> 2x – 20 + 20 = 40 + 20
→ 2x = 60
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Statement 5: x = 30
✔ Reason: Division Property of Equality
Divide both sides by 2:
> 2x ÷ 2 = 60 ÷ 2
→ x = 30
*(Note: In the image, there’s an "X" drawn next to this line — but that appears to be a mistake or scribble. The correct final statement is x = 30, and it should be checked off
✔.)*
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##
✔ Final Answer:
x = 30
This is proven step-by-step using basic algebraic properties:
- Subtraction Property
- Distributive Property
- Addition Property
- Division Property
Each step follows logically from the previous one, which is the essence of a two-column proof.
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📌
Tip: In two-column proofs, always ask yourself:
> “What did I do to get from the previous line to this one?”
That’s your reason!
Let me know if you’d like to see a visual diagram or practice more examples!
Parent Tip: Review the logic above to help your child master the concept of geometry worksheet beginning proofs answers.
