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

Answer :

To solve a linear equation that represents a model, where circles and a square are shown evenly balanced on a balance beam, we can follow these steps:

1. Understand the equation: We are given the equation [tex]\(x + 7 = 12\)[/tex]. This represents a scenario where a certain value [tex]\(x\)[/tex] added to 7 results in a total of 12.

2. Solve for [tex]\(x\)[/tex]:
- To isolate [tex]\(x\)[/tex], subtract 7 from both sides of the equation.
- The equation becomes [tex]\(x + 7 - 7 = 12 - 7\)[/tex], simplifying to [tex]\(x = 5\)[/tex].

3. Verify the solution:
- Substitute [tex]\(x = 5\)[/tex] back into the original equation [tex]\(x + 7 = 12\)[/tex].
- When [tex]\(x = 5\)[/tex], replacing [tex]\(x\)[/tex] gives [tex]\(5 + 7 = 12\)[/tex].
- Since both sides of the equation equal 12, the solution is verified as correct.

So, the correct representation and solution for the balance beam model is [tex]\(x + 7 = 12\)[/tex] where [tex]\(x = 5\)[/tex]. This corresponds to option 1.