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------------------------------------------------ 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 + 7 = 5 ; x = -2[/tex]
B. [tex]x = 5 + 7 ; x = 12[/tex]
C. [tex]x + 7 = 12 ; x = 5[/tex]
D. [tex]x + 5 = 7 ; x = 2[/tex]

To solve this problem, we need to create and solve a linear equation based on the balance model described. The options provided suggest different algebraic equations, and we're tasked with identifying the correct one.

Let's evaluate the option:

Equation: [tex]$ x + 7 = 12 $[/tex]

Solution:

1. Understanding the problem: This equation represents a situation where we have something (perhaps a weight represented by [tex]$ x $[/tex]) and an added weight of 7, which together balance out to 12.

2. Isolating [tex]$ x $[/tex]: We want to find the value of [tex]$ x $[/tex] that makes this equation true.

3. Solving the equation:

- Start with the equation:
[tex]$ x + 7 = 12 $[/tex]

- To isolate [tex]$ x $[/tex], subtract 7 from both sides:
[tex]$ x + 7 - 7 = 12 - 7 $[/tex]

- Simplifying both sides gives:
[tex]$ x = 5 $[/tex]

The solution for [tex]$ x $[/tex] is 5. Therefore, the choice with the equation [tex]$ x + 7 = 12 ; x = 5 $[/tex] is the correct one.