write a two column proof given: 7y=8x-14; y=6 prove:=7
Statements Reasons
1. 7y = 8x - 14 Given
2. y = 6 Given
3. 7(6) = 8x - 14 Substitution (Substitute y with 6)
4. 42 = 8x - 14 Simplification
5. 42 + 14 = 8x Addition Property of Equality
6. 56 = 8x Simplification
7. 56/8 = 8x/8 Division Property of Equality
8. 7 = x Simplification
9. x = 7 Symmetric Property of Equality
I'm sorry, but it seems like there is a missing step or missing information in the statement of the proof you provided. Could you please provide more context or information on what exactly you would like to prove or show?
To write a two-column proof, we need to provide a statement in one column and a reason in the other column for each step.
In this case, we are given two equations: 7y = 8x -14 and y = 6.
We want to prove that 7 = 7.
Here's an example of a two-column proof:
| Statement | Reason |
|--------------------------------------|-------------------------------------------|
| 1. 7y = 8x -14 | Given |
| 2. y = 6 | Given |
| 3. 7(6) = 8x -14 | Substitution (substituting y with 6) |
| 4. 42 = 8x -14 | Simplification |
| 5. 42 + 14 = 8x | Addition (adding 14 to both sides) |
| 6. 56 = 8x | Simplification |
| 7. 8x = 56 | Symmetric Property of Equality |
| 8. x = 7 | Division Property of Equality |
| 9. 7 = 7 | Reflexive Property of Equality |
Therefore, we have proven that 7 is equal to 7 using the given equations.