Write a two column proof.
-If XZ=ZY,XZ=4x+1,and ZY=6x-13, then x=7.
Statements: Reason:
1.XZ=ZY,XZ=4x+1 and ZY=6x-13 1.Given
That as far as I got to ^. Thanks
Statements: Reason:
1. XZ=ZY 1. Given
2. XZ=4x+1 2. Given
3. ZY=6x-13 3. Given
4. 4x+1=6x-13 4. Transitive Property (equating XZ and ZY)
5. -2x=-14 5. Subtract 4x from both sides
6. x=7 6. Divide both sides by -2
Therefore, if XZ=ZY, XZ=4x+1, and ZY=6x-13, then x=7.
Statements: Reason:
1. XZ = ZY, XZ = 4x + 1, and ZY = 6x - 13 Given
2. 4x + 1 = 6x - 13 Transitive Property
3. 13 - 1 = 6x - 4x Subtract 4x from both sides and add 13 to both sides
4. 12 = 2x Simplify
5. 12/2 = 2x/2 Divide both sides by 2
6. 6 = x Simplify
Therefore, if XZ = ZY, XZ = 4x + 1, and ZY = 6x - 13, then x = 6.
To complete the two-column proof, we need to provide the sequence of logical steps or reasons that lead us to the conclusion that x = 7. Let's continue:
Statements: Reasons:
1. XZ = ZY 1. Given
2. XZ = 4x + 1 2. Given
3. ZY = 6x - 13 3. Given
4. 4x + 1 = 6x - 13 4. Substitution (Equating XZ and ZY)
5. 14 = 2x 5. Simplification (Combining like terms)
6. 7 = x 6. Division by 2
Therefore, if XZ = ZY, XZ = 4x + 1, and ZY = 6x - 13, then x = 7.