Select the correct answer.

Create and solve a linear equation that represents the model, where circles and a square are shown evenly balanced on a balance beam.

A. [tex]x = 5 + 7 \; ; \; x = 12[/tex]

B. [tex]x + 7 = 12 \; ; \; x = 5[/tex]

C. [tex]x + 7 = 5 \; ; \; x = -2[/tex]

D. [tex]x + 5 = 7 \; ; \; x = 2[/tex]

Let's solve the problem by creating a linear equation and finding the solution.

We are given four options for linear equations and their solutions. We need to find the correct equation and solve it.

1. Equation: [tex]\( x = 5 + 7 \)[/tex]
- This simplifies to [tex]\( x = 12 \)[/tex]. But this does not align with the balance model where you solve for [tex]\( x \)[/tex] by isolating it from other numbers.

2. Equation: [tex]\( x + 7 = 12 \)[/tex]
- To solve for [tex]\( x \)[/tex], you need to isolate [tex]\( x \)[/tex] by subtracting 7 from both sides:
[tex]\[
x + 7 - 7 = 12 - 7
\][/tex]
[tex]\[
x = 5
\][/tex]

3. Equation: [tex]\( x + 7 = 5 \)[/tex]
- To solve for [tex]\( x \)[/tex], subtract 7 from both sides:
[tex]\[
x + 7 - 7 = 5 - 7
\][/tex]
[tex]\[
x = -2
\][/tex]

4. Equation: [tex]\( x + 5 = 7 \)[/tex]
- To solve for [tex]\( x \)[/tex], subtract 5 from both sides:
[tex]\[
x + 5 - 5 = 7 - 5
\][/tex]
[tex]\[
x = 2
\][/tex]

The correct answer, based on solving the equation and matching the model, is the second option:

[tex]\( x + 7 = 12 \)[/tex] ; [tex]\( x = 5 \)[/tex]