Answer :
- Solve each equation for $x$.
- Equation 1, 2, and 3 result in $x = 5$.
- Equation 4 results in $x = -5$.
- Therefore, equation 4 gives a different value for $x$: $\boxed{8.3-0.6 x=11.3}$.
### Explanation
1. Problem Analysis
We are given four equations and asked to find the one that gives a different value for $x$ when solved. Let's solve each equation for $x$.
2. Solving Equation 1
Equation 1: $8.3 = -0.6x + 11.3$. We can rearrange this to isolate $x$:
$0.6x = 11.3 - 8.3$
$0.6x = 3$
$x = \frac{3}{0.6} = 5$
3. Solving Equation 2
Equation 2: $11.3 = 8.3 + 0.6x$. Similarly, we isolate $x$:
$0.6x = 11.3 - 8.3$
$0.6x = 3$
$x = \frac{3}{0.6} = 5$
4. Solving Equation 3
Equation 3: $11.3 - 0.6x = 8.3$. Isolating $x$:
$0.6x = 11.3 - 8.3$
$0.6x = 3$
$x = \frac{3}{0.6} = 5$
5. Solving Equation 4
Equation 4: $8.3 - 0.6x = 11.3$. Isolating $x$:
$0.6x = 8.3 - 11.3$
$0.6x = -3$
$x = \frac{-3}{0.6} = -5$
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
Understanding how to solve linear equations is crucial in many real-world scenarios, such as calculating the required dosage of medicine based on a patient's weight, determining the amount of ingredients needed for a recipe based on the number of servings, or calculating the trajectory of a projectile in physics. In each of these cases, setting up and solving a linear equation allows us to find the unknown quantity and make informed decisions.
- Equation 1, 2, and 3 result in $x = 5$.
- Equation 4 results in $x = -5$.
- Therefore, equation 4 gives a different value for $x$: $\boxed{8.3-0.6 x=11.3}$.
### Explanation
1. Problem Analysis
We are given four equations and asked to find the one that gives a different value for $x$ when solved. Let's solve each equation for $x$.
2. Solving Equation 1
Equation 1: $8.3 = -0.6x + 11.3$. We can rearrange this to isolate $x$:
$0.6x = 11.3 - 8.3$
$0.6x = 3$
$x = \frac{3}{0.6} = 5$
3. Solving Equation 2
Equation 2: $11.3 = 8.3 + 0.6x$. Similarly, we isolate $x$:
$0.6x = 11.3 - 8.3$
$0.6x = 3$
$x = \frac{3}{0.6} = 5$
4. Solving Equation 3
Equation 3: $11.3 - 0.6x = 8.3$. Isolating $x$:
$0.6x = 11.3 - 8.3$
$0.6x = 3$
$x = \frac{3}{0.6} = 5$
5. Solving Equation 4
Equation 4: $8.3 - 0.6x = 11.3$. Isolating $x$:
$0.6x = 8.3 - 11.3$
$0.6x = -3$
$x = \frac{-3}{0.6} = -5$
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
Understanding how to solve linear equations is crucial in many real-world scenarios, such as calculating the required dosage of medicine based on a patient's weight, determining the amount of ingredients needed for a recipe based on the number of servings, or calculating the trajectory of a projectile in physics. In each of these cases, setting up and solving a linear equation allows us to find the unknown quantity and make informed decisions.
