Question

6. Complete the two-column proof.

Given:x/6+2=15
Prove: x = 78
Statement: x/6+2=15 Reason: A:
x/6=13 B:
x=78 C:

Answer 1

To solve for x, subtract 2 from both sides of the equation, then multiply both sides by 6. This yields that x equals 78, completing the proof.

Step-by-step explanation:

To complete the two-column proof, we start with what is given and use algebraic manipulation to prove that x equals 78. Here are the steps formatted into a proof:

1. Statement: x/6 + 2 = 15
   Reason: Given
2. Statement: x/6 = 15 - 2
   Reason: Subtraction Property of Equality
3. Statement: x/6 = 13
   Reason: Simplification
4. Statement: x = 13 × 6
   Reason: Multiplication Property of Equality
5. Statement: x = 78
   Reason: Simplification

Answer 2

Given:
`(x)/(6) + 2 = 15` ......[1]

To prove : x =78

Subtraction property states that you subtract the same number to both sides of an equation.

Subtract 2 from both sides of an equation [1];

`(x)/(6) + 2 - 2= 15 -2`

Simplify:

`(x)/(6) = 13` ......[2]

Multiplication property states that you multiply the same number to both sides of an equation.

Multiply 6 to both sides of an equation [2];

`(x)/(6) * 6 = 13 * 6`

Simplify:

`x = 78` proved!

Statement Reason

1.
`(x)/(6) + 2 = 15` Given

2.
`(x)/(6) = 13` Subtraction property of equality

3.
`x = 78` Multiplication property of equality