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 = 12 ; x = 5[/tex]

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

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

Answer :

Let's review and solve each of the provided equations step-by-step to determine the correct one.

1. Option 1: [tex]\( x + 5 = 7 \)[/tex]
To solve for [tex]\( x \)[/tex]:
[tex]\[
x + 5 = 7
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = 7 - 5
\][/tex]
[tex]\[
x = 2
\][/tex]
The solution is [tex]\( x = 2 \)[/tex].

2. Option 2: [tex]\( x + 7 = 12 \)[/tex]
To solve for [tex]\( x \)[/tex]:
[tex]\[
x + 7 = 12
\][/tex]
Subtract 7 from both sides:
[tex]\[
x = 12 - 7
\][/tex]
[tex]\[
x = 5
\][/tex]
The solution is [tex]\( x = 5 \)[/tex].

3. Option 3: [tex]\( x = 5 + 7 \)[/tex]
This equation is already solved. We simply perform the addition:
[tex]\[
x = 5 + 7
\][/tex]
[tex]\[
x = 12
\][/tex]
The solution is [tex]\( x = 12 \)[/tex].

4. Option 4: [tex]\( x + 7 = 5 \)[/tex]
To solve for [tex]\( x \)[/tex]:
[tex]\[
x + 7 = 5
\][/tex]
Subtract 7 from both sides:
[tex]\[
x = 5 - 7
\][/tex]
[tex]\[
x = -2
\][/tex]
The solution is [tex]\( x = -2 \)[/tex].

After solving all the options, we see:

- Option 1: [tex]\( x = 2 \)[/tex]
- Option 2: [tex]\( x = 5 \)[/tex]
- Option 3: [tex]\( x = 12 \)[/tex]
- Option 4: [tex]\( x = -2 \)[/tex]

Therefore, the correct linear equation that represents the model and its solution is:

- Option 2: [tex]\( x + 7 = 12 \)[/tex] ; [tex]\( x = 5 \)[/tex]

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