complete the two-column proof
given: x/6+2=15
prove: x=78
Given: x/6 + 2 = 15.
Prove: X = 78.
1. In the given Eq, substitute 78 for X. Reason: A quantity can be substituted for it's equal.
78/6 + 2 = 15,
13 + 2 = 15,
15 = 15.
amongus
To complete the two-column proof, we need to show the logical steps we took to determine that the value of x is 78 given the equation x/6 + 2 = 15. Here is a step-by-step breakdown of the proof:
Statement | Reason
------------------------------------------------
1. x/6 + 2 = 15 | Given
2. x/6 = 15 - 2 | Subtract 2 from both sides
3. x/6 = 13 | Simplify
4. x = 13 * 6 | Multiply both sides by 6
5. x = 78 | Simplify
Therefore, using the given equation, we have proved that x = 78 by following the logical steps.
To complete the two-column proof, we need to show step-by-step how we arrive at the conclusion that x equals 78 based on the given equation x/6 + 2 = 15. Here's how we can do it:
| Statements | Reasons |
|----------------|-------------|
| 1. Given: x/6 + 2 = 15 | |
| 2. Subtract 2 from both sides: x/6 + 2 - 2 = 15 - 2 | Subtraction Property of Equality |
| 3. Simplify: x/6 = 13 | Simplification |
| 4. Multiply both sides by 6: 6 * (x/6) = 13 * 6 | Multiplication Property of Equality |
| 5. Simplify: x = 78 | Simplification |
In the proof, we started with the given equation and used properties of equality to manipulate the equation and gradually solve for x. Note that all steps are justified by a reasoning principle or property. Thus, we have proven that x = 78 based on the given equation.