Answer :
To solve this problem, we're asked to select the correct linear equation and solve it. The key is finding the equation that correctly represents the given model of a balance beam with circles and a square.
Let's go through the options:
1. Option 1: [tex]\(x + 7 = 12\)[/tex]
- This equation says that if we add 7 to [tex]\(x\)[/tex], it equals 12.
- To solve for [tex]\(x\)[/tex], subtract 7 from both sides:
[tex]\[
x = 12 - 7
\][/tex]
[tex]\[
x = 5
\][/tex]
- This gives us [tex]\(x = 5\)[/tex], which is a possible solution.
2. Option 2: [tex]\(x + 5 = 7\)[/tex]
- This equation says that if we add 5 to [tex]\(x\)[/tex], it equals 7.
- To solve for [tex]\(x\)[/tex], subtract 5 from both sides:
[tex]\[
x = 7 - 5
\][/tex]
[tex]\[
x = 2
\][/tex]
- This gives us [tex]\(x = 2\)[/tex].
3. Option 3: [tex]\(x + 7 = 5\)[/tex]
- This equation says that if we add 7 to [tex]\(x\)[/tex], it equals 5.
- To solve for [tex]\(x\)[/tex], subtract 7 from both sides:
[tex]\[
x = 5 - 7
\][/tex]
[tex]\[
x = -2
\][/tex]
- This gives us [tex]\(x = -2\)[/tex].
4. Option 4: [tex]\(x = 5 + 7\)[/tex]
- This equation directly states that [tex]\(x\)[/tex] is equal to 5 plus 7.
- Performing the addition:
[tex]\[
x = 12
\][/tex]
- This gives us [tex]\(x = 12\)[/tex].
Based on these calculations, the correct linear equation and its solution from the options provided is:
Option 1: [tex]\(x + 7 = 12\)[/tex] with [tex]\(x = 5\)[/tex].
Let's go through the options:
1. Option 1: [tex]\(x + 7 = 12\)[/tex]
- This equation says that if we add 7 to [tex]\(x\)[/tex], it equals 12.
- To solve for [tex]\(x\)[/tex], subtract 7 from both sides:
[tex]\[
x = 12 - 7
\][/tex]
[tex]\[
x = 5
\][/tex]
- This gives us [tex]\(x = 5\)[/tex], which is a possible solution.
2. Option 2: [tex]\(x + 5 = 7\)[/tex]
- This equation says that if we add 5 to [tex]\(x\)[/tex], it equals 7.
- To solve for [tex]\(x\)[/tex], subtract 5 from both sides:
[tex]\[
x = 7 - 5
\][/tex]
[tex]\[
x = 2
\][/tex]
- This gives us [tex]\(x = 2\)[/tex].
3. Option 3: [tex]\(x + 7 = 5\)[/tex]
- This equation says that if we add 7 to [tex]\(x\)[/tex], it equals 5.
- To solve for [tex]\(x\)[/tex], subtract 7 from both sides:
[tex]\[
x = 5 - 7
\][/tex]
[tex]\[
x = -2
\][/tex]
- This gives us [tex]\(x = -2\)[/tex].
4. Option 4: [tex]\(x = 5 + 7\)[/tex]
- This equation directly states that [tex]\(x\)[/tex] is equal to 5 plus 7.
- Performing the addition:
[tex]\[
x = 12
\][/tex]
- This gives us [tex]\(x = 12\)[/tex].
Based on these calculations, the correct linear equation and its solution from the options provided is:
Option 1: [tex]\(x + 7 = 12\)[/tex] with [tex]\(x = 5\)[/tex].
