Write a two-column proof.
Given: 7y = 8x – 14; y = 6
Prove: x = 7
If a "two -column proof" looks something like this:
7y = 8x - 14, but y = 6
8x - 14 = 42
8x = 56
x = 7
To prove the given statement, "x = 7," we can use the property of equality.
Here is a two-column proof:
| Statements | Reasons |
|------------------------|--------------------------------------|
| 7y = 8x – 14 | Given |
| y = 6 | Given |
| 7(6) = 8x – 14 | Substitute y with 6 |
| 42 = 8x – 14 | Simplify the left side |
| 42 + 14 = 8x | Add 14 to both sides to isolate 8x |
| 56 = 8x | Simplify the left side |
| 56/8 = x | Divide both sides by 8 |
| 7 = x | Simplify the right side, 56/8 = 7/1 |
| x = 7 | Rewrite the equation with x first |
Therefore, the statement is proven: x = 7.