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

Let's solve the problem step by step to find out which linear equation accurately represents the model. We're given four options of linear equations, and we need to determine which one is correct by finding the value of [tex]$ x $[/tex].

1. Option 1:
- Equation: [tex]$ x + 7 = 12 $[/tex]
- Solve for [tex]$ x $[/tex]:
[tex]\[
x = 12 - 7
\][/tex]
[tex]\[
x = 5
\][/tex]
This option is correct because substituting [tex]$ x = 5 $[/tex] satisfies the equation.

2. Option 2:
- Equation: [tex]$ x = 5 + 7 $[/tex]
- Solve for [tex]$ x $[/tex]:
[tex]\[
x = 12
\][/tex]
This gives [tex]$ x = 12 $[/tex], but it doesn't match our target equation of balancing since the original equation is [tex]$ x + 7 = \text{some number} $[/tex].

3. Option 3:
- Equation: [tex]$ x + 7 = 5 $[/tex]
- Solve for [tex]$ x $[/tex]:
[tex]\[
x = 5 - 7
\][/tex]
[tex]\[
x = -2
\][/tex]
This is incorrect as we have a negative value and doesn't match any model satisfying our [tex]$ x $[/tex].

4. Option 4:
- Equation: [tex]$ x + 5 = 7 $[/tex]
- Solve for [tex]$ x $[/tex]:
[tex]\[
x = 7 - 5
\][/tex]
[tex]\[
x = 2
\][/tex]
This option provides [tex]$ x = 2 $[/tex] and matches its own setup but not the modeled balance.

The correct linear equation that represents the model is Option 1, where [tex]$ x + 7 = 12 $[/tex] with the solution [tex]$ x = 5 $[/tex].

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

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