High School

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

Answer :

To solve the problem, we're looking at different options for linear equations. Let's analyze each option step by step:

1. Option: [tex]\( x + 7 = 5 \)[/tex]
- Subtract 7 from both sides to isolate [tex]\( x \)[/tex]:
[tex]\[
x = 5 - 7 = -2
\][/tex]

2. Option: [tex]\( x = 5 + 7 \)[/tex]
- Simplify the right side:
[tex]\[
x = 12
\][/tex]

3. Option: [tex]\( x + 7 = 12 \)[/tex]
- Subtract 7 from both sides to solve for [tex]\( x \)[/tex]:
[tex]\[
x = 12 - 7 = 5
\][/tex]

4. Option: [tex]\( x + 5 = 7 \)[/tex]
- Subtract 5 from both sides to find [tex]\( x \)[/tex]:
[tex]\[
x = 7 - 5 = 2
\][/tex]

After evaluating these options, the correct choice that satisfies the given information is the one where the equation is [tex]\( x + 7 = 12 \)[/tex], and the solution is [tex]\( x = 5 \)[/tex].

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