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Answer :
To solve a linear equation that represents a model, where circles and a square are shown evenly balanced on a balance beam, we can follow these steps:
1. Understand the equation: We are given the equation [tex]\(x + 7 = 12\)[/tex]. This represents a scenario where a certain value [tex]\(x\)[/tex] added to 7 results in a total of 12.
2. Solve for [tex]\(x\)[/tex]:
- To isolate [tex]\(x\)[/tex], subtract 7 from both sides of the equation.
- The equation becomes [tex]\(x + 7 - 7 = 12 - 7\)[/tex], simplifying to [tex]\(x = 5\)[/tex].
3. Verify the solution:
- Substitute [tex]\(x = 5\)[/tex] back into the original equation [tex]\(x + 7 = 12\)[/tex].
- When [tex]\(x = 5\)[/tex], replacing [tex]\(x\)[/tex] gives [tex]\(5 + 7 = 12\)[/tex].
- Since both sides of the equation equal 12, the solution is verified as correct.
So, the correct representation and solution for the balance beam model is [tex]\(x + 7 = 12\)[/tex] where [tex]\(x = 5\)[/tex]. This corresponds to option 1.
1. Understand the equation: We are given the equation [tex]\(x + 7 = 12\)[/tex]. This represents a scenario where a certain value [tex]\(x\)[/tex] added to 7 results in a total of 12.
2. Solve for [tex]\(x\)[/tex]:
- To isolate [tex]\(x\)[/tex], subtract 7 from both sides of the equation.
- The equation becomes [tex]\(x + 7 - 7 = 12 - 7\)[/tex], simplifying to [tex]\(x = 5\)[/tex].
3. Verify the solution:
- Substitute [tex]\(x = 5\)[/tex] back into the original equation [tex]\(x + 7 = 12\)[/tex].
- When [tex]\(x = 5\)[/tex], replacing [tex]\(x\)[/tex] gives [tex]\(5 + 7 = 12\)[/tex].
- Since both sides of the equation equal 12, the solution is verified as correct.
So, the correct representation and solution for the balance beam model is [tex]\(x + 7 = 12\)[/tex] where [tex]\(x = 5\)[/tex]. This corresponds to option 1.
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