Complete the two-column proof.

Given: [tex]\frac{x}{6} + 2 = 15[/tex]
Prove: [tex]x = 78[/tex]

| Statement | Reason |
|-------------------------|--------------------------|
| [tex]\frac{x}{6} + 2 = 15[/tex] | Given |
| [tex]\frac{x}{6} = 13[/tex] | Subtract 2 from both sides |
| [tex]x = 78[/tex] | Multiply both sides by 6 |

(3 points)



Answer :

Sure! Let's complete the two-column proof for this equation [tex]\(\frac{x}{6}+2=15\)[/tex] to show that [tex]\(x\)[/tex] is indeed 78.

| Statements | Reasons |
|-----------------------------|-----------------------------------------|
| 1. [tex]\(\frac{x}{6}+2=15\)[/tex] | Given |
| 2. [tex]\(\frac{x}{6} = 13\)[/tex] | Subtract 2 from both sides |
| 3. [tex]\(x = 78\)[/tex] | Multiply both sides by 6 |

Let's break it down further with justifications for each step:

1. Given: The initial equation is [tex]\(\frac{x}{6} + 2 = 15\)[/tex].

2. Subtract 2 from both sides: To isolate the term with [tex]\(x\)[/tex], subtract 2 from each side of the equation:
[tex]\[ \frac{x}{6} + 2 - 2 = 15 - 2 \][/tex]
Simplifying both sides, we get:
[tex]\[ \frac{x}{6} = 13 \][/tex]

3. Multiply both sides by 6: To completely solve for [tex]\(x\)[/tex], multiply each side of the equation by 6:
[tex]\[ 6 \left(\frac{x}{6}\right) = 13 \cdot 6 \][/tex]
This simplifies to:
[tex]\[ x = 78 \][/tex]

Thus, by the end of these steps, we have proven that [tex]\(x = 78\)[/tex].