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

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

Answer :

To solve the problem, we need to select the correct linear equation that represents the balance model described.

First, let's look at the given choices and solve each one to determine which one results in the correct balance:

1. Equation: [tex]\(x + 7 = 12\)[/tex]
- To solve this, we need to isolate [tex]\(x\)[/tex].
- Subtract 7 from both sides:
[tex]\[
x + 7 - 7 = 12 - 7
\][/tex]
Simplifying gives:
[tex]\[
x = 5
\][/tex]

2. Equation: [tex]\(x = 5 + 7\)[/tex]
- Solve for [tex]\(x\)[/tex]:
[tex]\[
x = 5 + 7
\][/tex]
Simplifying gives:
[tex]\[
x = 12
\][/tex]

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

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

Among the given options, the first choice, [tex]\(x + 7 = 12\)[/tex], results in [tex]\(x = 5\)[/tex], which matches the result.

Thus, the correct equation representing the model is [tex]\(x + 7 = 12\)[/tex], and the solution is [tex]\(x = 5\)[/tex].

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