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 solve each of the options step-by-step to find out which equation and solution are correct:

1. Option 1: [tex]\( x + 7 = 12 \)[/tex]
To solve for [tex]\( x \)[/tex], we need to isolate [tex]\( x \)[/tex] on one side of the equation:
[tex]\[
x + 7 = 12
\][/tex]
Subtract 7 from both sides:
[tex]\[
x = 12 - 7
\][/tex]
[tex]\[
x = 5
\][/tex]
So, option 1 is correct since when [tex]\( x = 5 \)[/tex], the equation [tex]\( x + 7 = 12 \)[/tex] is satisfied.

2. Option 2: [tex]\( x + 5 = 7 \)[/tex]
Let's solve for [tex]\( x \)[/tex] by isolating it:
[tex]\[
x + 5 = 7
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = 7 - 5
\][/tex]
[tex]\[
x = 2
\][/tex]
This option is correct, too, since substituting [tex]\( x = 2 \)[/tex] satisfies the equation [tex]\( x + 5 = 7 \)[/tex].

3. Option 3: [tex]\( x + 7 = 5 \)[/tex]
Solve for [tex]\( x \)[/tex] as follows:
[tex]\[
x + 7 = 5
\][/tex]
Subtract 7 from both sides:
[tex]\[
x = 5 - 7
\][/tex]
[tex]\[
x = -2
\][/tex]
This solution is correct as well, confirming [tex]\( x + 7 = 5 \)[/tex] when [tex]\( x = -2 \)[/tex].

4. Option 4: [tex]\( x = 5 + 7 \)[/tex]
Solve the right side:
[tex]\[
x = 5 + 7
\][/tex]
[tex]\[
x = 12
\][/tex]
This option is correct because [tex]\( x = 12 \)[/tex] directly satisfies the equation.

Each of these options is calculated correctly, and they all match their respective solutions as given in the question.

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