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 = 2[/tex]

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

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

D. [tex]x = 5 + 7; \, x = 12[/tex]

Answer :

Let's go through each option step-by-step to find out which equations are correctly solved.

1. First equation: [tex]\(x + 5 = 7\)[/tex]
- To solve for [tex]\(x\)[/tex], subtract 5 from both sides:
[tex]\[
x = 7 - 5 = 2
\][/tex]
- The solution [tex]\(x = 2\)[/tex] is correct for this equation.

2. Second equation: [tex]\(x + 7 = 5\)[/tex]
- To find [tex]\(x\)[/tex], subtract 7 from both sides:
[tex]\[
x = 5 - 7 = -2
\][/tex]
- The solution [tex]\(x = -2\)[/tex] is correct for this equation.

3. Third equation: [tex]\(x + 7 = 12\)[/tex]
- Subtract 7 from both sides to solve for [tex]\(x\)[/tex]:
[tex]\[
x = 12 - 7 = 5
\][/tex]
- The solution [tex]\(x = 5\)[/tex] is correct for this equation.

4. Fourth equation: [tex]\(x = 5 + 7\)[/tex]
- Calculate the right side:
[tex]\[
x = 12
\][/tex]
- The solution [tex]\(x = 12\)[/tex] is correct for this equation.

All the given equations and their solutions are correctly calculated.

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