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

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

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

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

Answer :

To solve the given problem, we're dealing with a scenario where we need to create and solve a linear equation. Among the options provided, we're trying to find a balance where the equation is correctly set and solved.

Let's break down the given options to find the right equation and solution:

1. Option: [tex]\(x + 5 = 7 ; x = 2\)[/tex]
- Solve [tex]\(x + 5 = 7\)[/tex]:
- Subtract 5 from both sides: [tex]\(x = 7 - 5 = 2\)[/tex]
- This solution is correct for the equation [tex]\(x + 5 = 7\)[/tex].

2. Option: [tex]\(x = 5 + 7 ; x = 12\)[/tex]
- This is not a balanced equation setup initially and does not match the context of finding a solution through solving.

3. Option: [tex]\(x + 7 = 12 ; x = 5\)[/tex]
- Solve [tex]\(x + 7 = 12\)[/tex]:
- Subtract 7 from both sides: [tex]\(x = 12 - 7 = 5\)[/tex]
- This solution is correct for the equation [tex]\(x + 7 = 12\)[/tex].

4. Option: [tex]\(x + 7 = 5 ; x = -2\)[/tex]
- Solve [tex]\(x + 7 = 5\)[/tex]:
- Subtract 7 from both sides: [tex]\(x = 5 - 7 = -2\)[/tex]
- This solution is correct for the equation [tex]\(x + 7 = 5\)[/tex].

The correct choice, considering the true numerical result, is:

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

This means the solution to the problem is verifying the equation [tex]\(x + 7 = 12\)[/tex] and solving it to get the value [tex]\(x = 5\)[/tex].

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Rewritten by : Barada