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Answer :
Let's go through each option step-by-step to find the correct linear equation that solves the problem of circles and a square equally balancing on a balance beam.
1. First Option: [tex]\( x + 7 = 5 \)[/tex]; [tex]\( x = -2 \)[/tex]
- Solve the equation [tex]\( x + 7 = 5 \)[/tex].
- Subtract 7 from both sides: [tex]\( x = 5 - 7 \)[/tex].
- Calculate: [tex]\( x = -2 \)[/tex].
- Since [tex]\( x = -2 \)[/tex], the equation is correct and balanced.
2. Second Option: [tex]\( x + 5 = 7 \)[/tex]; [tex]\( x = 2 \)[/tex]
- Solve the equation [tex]\( x + 5 = 7 \)[/tex].
- Subtract 5 from both sides: [tex]\( x = 7 - 5 \)[/tex].
- Calculate: [tex]\( x = 2 \)[/tex].
- Since [tex]\( x = 2 \)[/tex], the equation is correct and balanced.
3. Third Option: [tex]\( x + 7 = 12 \)[/tex]; [tex]\( x = 5 \)[/tex]
- Solve the equation [tex]\( x + 7 = 12 \)[/tex].
- Subtract 7 from both sides: [tex]\( x = 12 - 7 \)[/tex].
- Calculate: [tex]\( x = 5 \)[/tex].
- Since [tex]\( x = 5 \)[/tex], the equation is correct and balanced.
4. Fourth Option: [tex]\( x = 5 + 7 \)[/tex]; [tex]\( x = 12 \)[/tex]
- Solve the equation [tex]\( x = 5 + 7 \)[/tex].
- Calculate: [tex]\( x = 12 \)[/tex].
- Since [tex]\( x = 12 \)[/tex], the equation is correct and balanced.
After verifying each option, we see that each choice represents a valid solution to different linear equations. However, we are looking for the original linear equation that describes balancing the circles and square. Analyzing the options, the balanced equation is correctly represented by:
- Third Option: [tex]\( x + 7 = 12 \)[/tex] with the solution [tex]\( x = 5 \)[/tex]
This option is the accurate representation of a balance model where the total weight balances as described.
1. First Option: [tex]\( x + 7 = 5 \)[/tex]; [tex]\( x = -2 \)[/tex]
- Solve the equation [tex]\( x + 7 = 5 \)[/tex].
- Subtract 7 from both sides: [tex]\( x = 5 - 7 \)[/tex].
- Calculate: [tex]\( x = -2 \)[/tex].
- Since [tex]\( x = -2 \)[/tex], the equation is correct and balanced.
2. Second Option: [tex]\( x + 5 = 7 \)[/tex]; [tex]\( x = 2 \)[/tex]
- Solve the equation [tex]\( x + 5 = 7 \)[/tex].
- Subtract 5 from both sides: [tex]\( x = 7 - 5 \)[/tex].
- Calculate: [tex]\( x = 2 \)[/tex].
- Since [tex]\( x = 2 \)[/tex], the equation is correct and balanced.
3. Third Option: [tex]\( x + 7 = 12 \)[/tex]; [tex]\( x = 5 \)[/tex]
- Solve the equation [tex]\( x + 7 = 12 \)[/tex].
- Subtract 7 from both sides: [tex]\( x = 12 - 7 \)[/tex].
- Calculate: [tex]\( x = 5 \)[/tex].
- Since [tex]\( x = 5 \)[/tex], the equation is correct and balanced.
4. Fourth Option: [tex]\( x = 5 + 7 \)[/tex]; [tex]\( x = 12 \)[/tex]
- Solve the equation [tex]\( x = 5 + 7 \)[/tex].
- Calculate: [tex]\( x = 12 \)[/tex].
- Since [tex]\( x = 12 \)[/tex], the equation is correct and balanced.
After verifying each option, we see that each choice represents a valid solution to different linear equations. However, we are looking for the original linear equation that describes balancing the circles and square. Analyzing the options, the balanced equation is correctly represented by:
- Third Option: [tex]\( x + 7 = 12 \)[/tex] with the solution [tex]\( x = 5 \)[/tex]
This option is the accurate representation of a balance model where the total weight balances as described.
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