Answer :
To solve the problem, let's consider each option and find the correct equation and solution.
1. Option 1: [tex]\( x = 5 + 7 \)[/tex]
- Here, you add 5 and 7.
- This gives us [tex]\( x = 12 \)[/tex].
2. Option 2: [tex]\( x + 7 = 5 \)[/tex]
- To solve for [tex]\( x \)[/tex], subtract 7 from both sides of the equation.
- This gives us [tex]\( x = 5 - 7 \)[/tex].
- So, [tex]\( x = -2 \)[/tex].
3. Option 3: [tex]\( x + 7 = 12 \)[/tex]
- To find [tex]\( x \)[/tex], subtract 7 from both sides.
- This gives us [tex]\( x = 12 - 7 \)[/tex].
- Thus, [tex]\( x = 5 \)[/tex].
4. Option 4: [tex]\( x + 5 = 7 \)[/tex]
- Subtract 5 from both sides to solve for [tex]\( x \)[/tex].
- This gives us [tex]\( x = 7 - 5 \)[/tex].
- So, [tex]\( x = 2 \)[/tex].
Now, let's compare the solutions with the balance scenario mentioned. A linear equation that models a balanced beam should demonstrate that all parts are equal when solved.
Out of the given options, [tex]\( x + 7 = 12 \)[/tex] is the equation that correctly models this scenario, resulting in [tex]\( x = 5 \)[/tex].
1. Option 1: [tex]\( x = 5 + 7 \)[/tex]
- Here, you add 5 and 7.
- This gives us [tex]\( x = 12 \)[/tex].
2. Option 2: [tex]\( x + 7 = 5 \)[/tex]
- To solve for [tex]\( x \)[/tex], subtract 7 from both sides of the equation.
- This gives us [tex]\( x = 5 - 7 \)[/tex].
- So, [tex]\( x = -2 \)[/tex].
3. Option 3: [tex]\( x + 7 = 12 \)[/tex]
- To find [tex]\( x \)[/tex], subtract 7 from both sides.
- This gives us [tex]\( x = 12 - 7 \)[/tex].
- Thus, [tex]\( x = 5 \)[/tex].
4. Option 4: [tex]\( x + 5 = 7 \)[/tex]
- Subtract 5 from both sides to solve for [tex]\( x \)[/tex].
- This gives us [tex]\( x = 7 - 5 \)[/tex].
- So, [tex]\( x = 2 \)[/tex].
Now, let's compare the solutions with the balance scenario mentioned. A linear equation that models a balanced beam should demonstrate that all parts are equal when solved.
Out of the given options, [tex]\( x + 7 = 12 \)[/tex] is the equation that correctly models this scenario, resulting in [tex]\( x = 5 \)[/tex].
