Answer :
To solve this problem, we need to create and solve a linear equation based on the balance model described. The options provided suggest different algebraic equations, and we're tasked with identifying the correct one.
Let's evaluate the option:
Equation: [tex]\( x + 7 = 12 \)[/tex]
Solution:
1. Understanding the problem: This equation represents a situation where we have something (perhaps a weight represented by [tex]\( x \)[/tex]) and an added weight of 7, which together balance out to 12.
2. Isolating [tex]\( x \)[/tex]: We want to find the value of [tex]\( x \)[/tex] that makes this equation true.
3. Solving the equation:
- Start with the equation:
[tex]\( x + 7 = 12 \)[/tex]
- To isolate [tex]\( x \)[/tex], subtract 7 from both sides:
[tex]\( x + 7 - 7 = 12 - 7 \)[/tex]
- Simplifying both sides gives:
[tex]\( x = 5 \)[/tex]
The solution for [tex]\( x \)[/tex] is 5. Therefore, the choice with the equation [tex]\( x + 7 = 12 ; x = 5 \)[/tex] is the correct one.
Let's evaluate the option:
Equation: [tex]\( x + 7 = 12 \)[/tex]
Solution:
1. Understanding the problem: This equation represents a situation where we have something (perhaps a weight represented by [tex]\( x \)[/tex]) and an added weight of 7, which together balance out to 12.
2. Isolating [tex]\( x \)[/tex]: We want to find the value of [tex]\( x \)[/tex] that makes this equation true.
3. Solving the equation:
- Start with the equation:
[tex]\( x + 7 = 12 \)[/tex]
- To isolate [tex]\( x \)[/tex], subtract 7 from both sides:
[tex]\( x + 7 - 7 = 12 - 7 \)[/tex]
- Simplifying both sides gives:
[tex]\( x = 5 \)[/tex]
The solution for [tex]\( x \)[/tex] is 5. Therefore, the choice with the equation [tex]\( x + 7 = 12 ; x = 5 \)[/tex] is the correct one.
