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

Let's examine each option to determine which ones correctly solve the equations provided:

1. Option A: [tex]$ x + 5 = 7 $[/tex]; Solve for [tex]$ x $[/tex]
- Start by isolating [tex]$ x $[/tex] on one side of the equation:
[tex]\[
x + 5 = 7
\][/tex]
- Subtract 5 from both sides:
[tex]\[
x = 7 - 5
\][/tex]
- Calculate:
[tex]\[
x = 2
\][/tex]
- Therefore, the solution [tex]$ x = 2 $[/tex] is correct for this equation.

2. Option B: [tex]$ x + 7 = 5 $[/tex]; Solve for [tex]$ x $[/tex]
- Isolate [tex]$ x $[/tex] by subtracting 7 from both sides of the equation:
[tex]\[
x + 7 = 5
\][/tex]
- Subtract 7:
[tex]\[
x = 5 - 7
\][/tex]
- Calculate:
[tex]\[
x = -2
\][/tex]
- Thus, the solution [tex]$ x = -2 $[/tex] is correct for this equation.

3. Option C: [tex]$ x = 5 + 7 $[/tex]; Solve for [tex]$ x $[/tex]
- Simply add the numbers on the right side:
[tex]\[
x = 5 + 7
\][/tex]
- Calculate:
[tex]\[
x = 12
\][/tex]
- Therefore, the solution [tex]$ x = 12 $[/tex] is correct.

4. Option D: [tex]$ x + 7 = 12 $[/tex]; Solve for [tex]$ x $[/tex]
- To solve for [tex]$ x $[/tex], subtract 7 from both sides:
[tex]\[
x + 7 = 12
\][/tex]
- Subtract 7:
[tex]\[
x = 12 - 7
\][/tex]
- Calculate:
[tex]\[
x = 5
\][/tex]
- Thus, the solution [tex]$ x = 5 $[/tex] is correct for this equation.

So, each option given has a matching solution that correctly solves the associated linear equation.

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

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