Given: x/4-7=y and y=2
Prove: x=36
Using two column proof.
Statement | Reason
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1. y = 2 | Given
2. x/4 - 7 = y | Given
3. x/4 - 7 = 2 | Substitution (from statement 1)
4. x/4 = 2 + 7 | Addition Property of Equality
5. x/4 = 9 | Simplification
6. x = 9 * 4 | Multiplication Property of Equality
7. x = 36 | Simplification (multiplication)
Step 1: Given: x/4-7=y
y=2
Prove: x=36
Step 2: Substitute y=2 into the equation x/4-7=y
x/4-7=2
Step 3: Add 7 to both sides of the equation to isolate x/4
x/4-7+7=2+7
x/4=9
Step 4: Multiply both sides of the equation by 4 to cancel out the fraction
4*(x/4)=9*4
(4/1)*(x/4)=36
Step 5: Simplify
x/1=36
x=36
Step 6: Conclusion: From the given equation x/4-7=y, when substituting y=2, we have obtained x=36. Therefore, the statement is proven.
To prove that x = 36 using a two-column proof, we need to start with the given equation and perform a series of logical steps until we arrive at the conclusion x = 36. Here's how you can do it:
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| Column 1 | Column 2 |
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| Given | x/4 - 7 = y |
| Given | y = 2 |
| Substitution | x/4 - 7 = 2 |
| Addition | x/4 = 9 |
| Multiplication | x = 36 |
| Conclusion | x = 36 |
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Column 1: Statements
Column 2: Reasons or Steps
1. Given: x/4 - 7 = y
- This is the given equation from the problem.
2. Given: y = 2
- This is the given equation from the problem.
3. Substitution: x/4 - 7 = 2
- Substitute y with its given value, which is 2.
4. Addition: x/4 = 9
- Add 7 to both sides of the equation to isolate the x/4 term.
5. Multiplication: x = 36
- Multiply both sides of the equation by 4 to isolate the x term.
6. Conclusion: x = 36
- This statement concludes that x is equal to 36, which is our desired result.
By following these logical steps and using algebraic manipulations, we have successfully proved that x = 36 based on the given equations.