write a two-column proof
Given 7y=8x-14;y=6
Prove x=7
Where do I start?
7y = 8x-14 given
7*6 = 8x-14 substitution
42 = 8x-14
42+14 = 8x equality of addition
56 = 8x
7 = x division equality
Thank you so much @anonymos
To start writing a two-column proof, you need to organize the given information and carefully follow a logical sequence of steps. Here's how you can proceed:
1. Write "Given" in the left column and state the given information: 7y = 8x - 14 and y = 6.
Given | Reason
7y = 8x - 14; y = 6 |
2. In the right column, provide a reason for each step.
Given | Reason
7y = 8x - 14; y = 6 | Given
3. We are aiming to prove that x = 7. To do this, we will substitute the value of y into the first equation.
Given | Reason
7y = 8x - 14; y = 6 | Given
7(6) = 8x - 14 | Substitution
4. Simplify the equation by performing the multiplication on the left side.
Given | Reason
7y = 8x - 14; y = 6 | Given
42 = 8x - 14 | Simplification
5. Add 14 to both sides of the equation to isolate the term with x.
Given | Reason
7y = 8x - 14; y = 6 | Given
42 + 14 = 8x - 14 + 14 | Addition
6. Simplify both sides of the equation.
Given | Reason
7y = 8x - 14; y = 6 | Given
56 = 8x | Simplification
7. Divide both sides of the equation by 8 to solve for x.
Given | Reason
7y = 8x - 14; y = 6 | Given
56 ÷ 8 = 8x ÷ 8 | Division
7 = x | Simplification
8. Therefore, x = 7 is proven.
Given | Reason
7y = 8x - 14; y = 6 | Given
7 = x | Conclusion
Note: In a two-column proof, the left column shows the steps you took, and the right column provides the reasons or justifications for each step. Remember to use proper mathematical notation and symbols to ensure clarity in your proof.