Answer :
- Solve each equation for $x$.
- Equation 1, 2, and 3 result in $x = 5$.
- Equation 4 results in $x = -5$.
- Therefore, 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 for $x$.
2. Solving Equation 1
Equation 1: $8.3 = -0.6x + 11.3$. Subtracting 11.3 from both sides gives $-3 = -0.6x$. Dividing both sides by -0.6 gives $x = \frac{-3}{-0.6} = 5$.
3. Solving Equation 2
Equation 2: $11.3 = 8.3 + 0.6x$. Subtracting 8.3 from both sides gives $3 = 0.6x$. Dividing both sides by 0.6 gives $x = \frac{3}{0.6} = 5$.
4. Solving Equation 3
Equation 3: $11.3 - 0.6x = 8.3$. Subtracting 11.3 from both sides gives $-0.6x = -3$. Dividing both sides by -0.6 gives $x = \frac{-3}{-0.6} = 5$.
5. Solving Equation 4
Equation 4: $8.3 - 0.6x = 11.3$. Subtracting 8.3 from both sides gives $-0.6x = 3$. Dividing both sides by -0.6 gives $x = \frac{3}{-0.6} = -5$.
6. Conclusion
Comparing the solutions, we see that equations 1, 2, and 3 all give $x = 5$, while equation 4 gives $x = -5$. Therefore, equation 4 results in a different value of $x$ than the other three.
### Examples
When designing a seesaw, understanding how equations change with different placements of weight is crucial. This problem demonstrates how a small change in an equation (like the sign) can dramatically affect the outcome, similar to how moving the fulcrum on a seesaw changes the balance. This concept is applicable in various engineering and physics problems where understanding the impact of variables is essential for predicting outcomes.
- Equation 1, 2, and 3 result in $x = 5$.
- Equation 4 results in $x = -5$.
- Therefore, 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 for $x$.
2. Solving Equation 1
Equation 1: $8.3 = -0.6x + 11.3$. Subtracting 11.3 from both sides gives $-3 = -0.6x$. Dividing both sides by -0.6 gives $x = \frac{-3}{-0.6} = 5$.
3. Solving Equation 2
Equation 2: $11.3 = 8.3 + 0.6x$. Subtracting 8.3 from both sides gives $3 = 0.6x$. Dividing both sides by 0.6 gives $x = \frac{3}{0.6} = 5$.
4. Solving Equation 3
Equation 3: $11.3 - 0.6x = 8.3$. Subtracting 11.3 from both sides gives $-0.6x = -3$. Dividing both sides by -0.6 gives $x = \frac{-3}{-0.6} = 5$.
5. Solving Equation 4
Equation 4: $8.3 - 0.6x = 11.3$. Subtracting 8.3 from both sides gives $-0.6x = 3$. Dividing both sides by -0.6 gives $x = \frac{3}{-0.6} = -5$.
6. Conclusion
Comparing the solutions, we see that equations 1, 2, and 3 all give $x = 5$, while equation 4 gives $x = -5$. Therefore, equation 4 results in a different value of $x$ than the other three.
### Examples
When designing a seesaw, understanding how equations change with different placements of weight is crucial. This problem demonstrates how a small change in an equation (like the sign) can dramatically affect the outcome, similar to how moving the fulcrum on a seesaw changes the balance. This concept is applicable in various engineering and physics problems where understanding the impact of variables is essential for predicting outcomes.
