High School

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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 [/tex]; [tex] x = 2 [/tex]

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

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

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

Answer :

Let's look at the linear equations provided in the options and solve each one step by step to find the correct answer:

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

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

3. Option 3: [tex]\( x = 5 + 7 \)[/tex]
- Simply add the numbers on the right side:
[tex]\[
x = 12
\][/tex]

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

The correct option based on the true result of [tex]\( x = 5 \)[/tex] is Option 2: [tex]\( x + 7 = 12 \)[/tex] ; x = 5.

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