College

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 = 12[/tex]

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

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

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

Answer :

Alright, let's go through each of the given linear equations and check step-by-step to see if their solutions are correct:

1. Equation: [tex]\( x = 5 + 7 \)[/tex]
- Solution: [tex]\( x = 12 \)[/tex]
- To verify, we calculate [tex]\( 5 + 7 \)[/tex]:
[tex]\[
5 + 7 = 12
\][/tex]
- Therefore, the solution [tex]\( x = 12 \)[/tex] is correct.

2. Equation: [tex]\( x + 7 = 5 \)[/tex]
- Solution: [tex]\( x = -2 \)[/tex]
- To verify, we isolate [tex]\( x \)[/tex] by subtracting 7 from both sides:
[tex]\[
x + 7 - 7 = 5 - 7 \implies x = -2
\][/tex]
- Therefore, the solution [tex]\( x = -2 \)[/tex] is correct.

3. Equation: [tex]\( x + 7 = 12 \)[/tex]
- Solution: [tex]\( x = 5 \)[/tex]
- To verify, we isolate [tex]\( x \)[/tex] by subtracting 7 from both sides:
[tex]\[
x + 7 - 7 = 12 - 7 \implies x = 5
\][/tex]
- Therefore, the solution [tex]\( x = 5 \)[/tex] is correct.

4. Equation: [tex]\( x + 5 = 7 \)[/tex]
- Solution: [tex]\( x = 2 \)[/tex]
- To verify, we isolate [tex]\( x \)[/tex] by subtracting 5 from both sides:
[tex]\[
x + 5 - 5 = 7 - 5 \implies x = 2
\][/tex]
- Therefore, the solution [tex]\( x = 2 \)[/tex] is correct.

Upon review, all the provided solutions are correct for their respective linear equations:

- [tex]\( x = 5 + 7 \rightarrow x = 12 \)[/tex]
- [tex]\( x + 7 = 5 \rightarrow x = -2 \)[/tex]
- [tex]\( x + 7 = 12 \rightarrow x = 5 \)[/tex]
- [tex]\( x + 5 = 7 \rightarrow x = 2 \)[/tex]

Therefore, the correct options for the given problem are:

1, 2, 3, and 4.

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