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Answer :
- Solve each equation for $x$.
- Equation 1, 2, and 3 result in $x = 5$.
- Equation 4 results in $x = -5$.
- Equation 4 yields a different value of $x$: $\boxed{8.3-0.6 x=11.3}$.
### Explanation
1. Problem Analysis
We are given four equations and asked to find the one that yields a different value for $x$ when solved. Let's solve each equation step by step.
2. Solving Equation 1
Equation 1: $8.3 = -0.6x + 11.3$. We want to isolate $x$. First, subtract 11.3 from both sides: $8.3 - 11.3 = -0.6x$, which simplifies to $-3 = -0.6x$. Now, divide both sides by -0.6: $x = \frac{-3}{-0.6} = 5$.
3. Solving Equation 2
Equation 2: $11.3 = 8.3 + 0.6x$. Subtract 8.3 from both sides: $11.3 - 8.3 = 0.6x$, which simplifies to $3 = 0.6x$. Now, divide both sides by 0.6: $x = \frac{3}{0.6} = 5$.
4. Solving Equation 3
Equation 3: $11.3 - 0.6x = 8.3$. Subtract 11.3 from both sides: $-0.6x = 8.3 - 11.3$, which simplifies to $-0.6x = -3$. Now, divide both sides by -0.6: $x = \frac{-3}{-0.6} = 5$.
5. Solving Equation 4
Equation 4: $8.3 - 0.6x = 11.3$. Subtract 8.3 from both sides: $-0.6x = 11.3 - 8.3$, which simplifies to $-0.6x = 3$. Now, divide both sides by -0.6: $x = \frac{3}{-0.6} = -5$.
6. Conclusion
Comparing the solutions, we see that equations 1, 2, and 3 all result in $x = 5$, while equation 4 results in $x = -5$. Therefore, equation 4 yields a different value of $x$.
### Examples
Understanding how to solve linear equations is crucial in many real-world scenarios, such as calculating the required dosage of medicine. For instance, if a certain medication requires a specific concentration in the bloodstream, doctors use linear equations to determine the correct amount to administer based on factors like the patient's weight and metabolism rate. This ensures that patients receive the right amount of medication to effectively treat their condition without causing harmful side effects.
- Equation 1, 2, and 3 result in $x = 5$.
- Equation 4 results in $x = -5$.
- Equation 4 yields a different value of $x$: $\boxed{8.3-0.6 x=11.3}$.
### Explanation
1. Problem Analysis
We are given four equations and asked to find the one that yields a different value for $x$ when solved. Let's solve each equation step by step.
2. Solving Equation 1
Equation 1: $8.3 = -0.6x + 11.3$. We want to isolate $x$. First, subtract 11.3 from both sides: $8.3 - 11.3 = -0.6x$, which simplifies to $-3 = -0.6x$. Now, divide both sides by -0.6: $x = \frac{-3}{-0.6} = 5$.
3. Solving Equation 2
Equation 2: $11.3 = 8.3 + 0.6x$. Subtract 8.3 from both sides: $11.3 - 8.3 = 0.6x$, which simplifies to $3 = 0.6x$. Now, divide both sides by 0.6: $x = \frac{3}{0.6} = 5$.
4. Solving Equation 3
Equation 3: $11.3 - 0.6x = 8.3$. Subtract 11.3 from both sides: $-0.6x = 8.3 - 11.3$, which simplifies to $-0.6x = -3$. Now, divide both sides by -0.6: $x = \frac{-3}{-0.6} = 5$.
5. Solving Equation 4
Equation 4: $8.3 - 0.6x = 11.3$. Subtract 8.3 from both sides: $-0.6x = 11.3 - 8.3$, which simplifies to $-0.6x = 3$. Now, divide both sides by -0.6: $x = \frac{3}{-0.6} = -5$.
6. Conclusion
Comparing the solutions, we see that equations 1, 2, and 3 all result in $x = 5$, while equation 4 results in $x = -5$. Therefore, equation 4 yields a different value of $x$.
### Examples
Understanding how to solve linear equations is crucial in many real-world scenarios, such as calculating the required dosage of medicine. For instance, if a certain medication requires a specific concentration in the bloodstream, doctors use linear equations to determine the correct amount to administer based on factors like the patient's weight and metabolism rate. This ensures that patients receive the right amount of medication to effectively treat their condition without causing harmful side effects.
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