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

Answer :

Sure! Let's solve the problem step by step.

We are given four options for linear equations, and we need to determine which one is correctly solved.

1. Option 1: [tex]\( x + 7 = 12 \)[/tex]

- To find the value of [tex]\( x \)[/tex], subtract 7 from both sides:
[tex]\[
x = 12 - 7
\][/tex]
[tex]\[
x = 5
\][/tex]

2. Option 2: [tex]\( x + 5 = 7 \)[/tex]

- Subtract 5 from both sides to solve for [tex]\( x \)[/tex]:
[tex]\[
x = 7 - 5
\][/tex]
[tex]\[
x = 2
\][/tex]

3. Option 3: [tex]\( x + 7 = 5 \)[/tex]

- Subtract 7 from both sides:
[tex]\[
x = 5 - 7
\][/tex]
[tex]\[
x = -2
\][/tex]

4. Option 4: [tex]\( x = 5 + 7 \)[/tex]

- Solve for [tex]\( x \)[/tex] by simply calculating the sum:
[tex]\[
x = 12
\][/tex]

After reviewing each option, we find that Option 1 [tex]\( x + 7 = 12 \)[/tex] gives us [tex]\( x = 5 \)[/tex]. This equation and its solution are correct.

Therefore, the correct equation and solution is:

[tex]\( x + 7 = 12 \)[/tex], and [tex]\( x = 5 \)[/tex].

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