(I need help finding the remaining reasons for each statement in the column proof, I already know the first two)
Finish the two-column Proof:
If AB = 5x, BC = 2x –4, and AC = 52, then x = 8.
(two column proof)
AB= 5x, BC = 2x -4, AC = 52 (Given)
52 = 5x + 2x -4 (Substitute)
52 + 4 = 7x
7x = 56
x = 56/7
x = 8
To complete the two-column proof and find the remaining reasons for each statement, here's how you can do it:
1. AB = 5x, BC = 2x - 4, AC = 52 (Given)
2. 52 = 5x + 2x - 4 (Substitute)
3. 52 + 4 = 7x (Add 4 to both sides to isolate the term with x)
4. 56 = 7x (Combine like terms)
5. 7x = 56 (Switch the sides to have the variable term on the left)
6. x = 56/7 (Divide both sides by 7 to isolate x)
7. x = 8 (Simplify)
So, the remaining reasons for each statement in the two-column proof are:
- Reason for statement 3: Addition Property of Equality (you added 4 to both sides of the equation)
- Reason for statement 4: Combining Like Terms (you combined the terms 52 and 4)
- Reason for statement 5: Transitive Property of Equality (you switched the sides of the equation)
- Reason for statement 6: Division Property of Equality (you divided both sides of the equation by 7)
- Reason for statement 7: Simplification (you simplified the expression 56/7 to 8)