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

Answer :

Sure! Let's go through the options step-by-step to solve the linear equations and determine the correct answer.

We have the following options to consider:

1. [tex]\( x = 5 + 7 \)[/tex]
2. [tex]\( x + 7 = 5 \)[/tex]
3. [tex]\( x + 5 = 7 \)[/tex]
4. [tex]\( x + 7 = 12 \)[/tex]

Let's examine each option separately:

1. Option 1:
[tex]\[
x = 5 + 7
\][/tex]
When you solve this, it simplifies to:
[tex]\[
x = 12
\][/tex]
This option implies [tex]\( x \)[/tex] is directly calculated to be 12.

2. Option 2:
[tex]\[
x + 7 = 5
\][/tex]
To find [tex]\( x \)[/tex], subtract 7 from both sides:
[tex]\[
x = 5 - 7 \\
x = -2
\][/tex]
This means [tex]\( x \)[/tex] equals -2.

3. Option 3:
[tex]\[
x + 5 = 7
\][/tex]
To solve for [tex]\( x \)[/tex], subtract 5 from both sides:
[tex]\[
x = 7 - 5 \\
x = 2
\][/tex]
So here, [tex]\( x \)[/tex] equals 2.

4. Option 4:
[tex]\[
x + 7 = 12
\][/tex]
To solve for [tex]\( x \)[/tex], subtract 7 from both sides:
[tex]\[
x = 12 - 7 \\
x = 5
\][/tex]
Here, [tex]\( x \)[/tex] is 5.

According to the information provided, the correct solution is [tex]\( x = 5 \)[/tex]. Therefore, the correct linear equation and its solution is:

[tex]\( x + 7 = 12 ; x = 5 \)[/tex]

Option 4 corresponds to this solution.

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