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

Answer :

Sure! Let's analyze each linear equation option step by step:

1. Equation: [tex]\(x + 7 = 12\)[/tex]
- To solve for [tex]\(x\)[/tex], you need to isolate [tex]\(x\)[/tex] on one side of the equation.
- Subtract 7 from both sides of the equation:
[tex]\[
x + 7 - 7 = 12 - 7
\][/tex]
[tex]\[
x = 5
\][/tex]
- The solution for [tex]\(x\)[/tex] in this equation is 5.

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

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

4. Equation: [tex]\(x = 5 + 7\)[/tex]
- Directly add 5 and 7:
[tex]\[
x = 5 + 7
\][/tex]
[tex]\[
x = 12
\][/tex]
- The solution for [tex]\(x\)[/tex] is 12.

Among these options, each represents a different linear equation and its solution. Identify the one that best fits your requirements or model description.

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