Answer :
Let's look at four different equations and determine which one gives a unique solution for [tex]\( x \)[/tex].
1. Equation 1: [tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
2. Equation 2: [tex]\( 11.3 = 83 + 0.6x \)[/tex]
3. Equation 3: [tex]\( 11.3 - 0.6x = 8.3 \)[/tex]
4. Equation 4: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
Now, let's solve each equation step by step.
### Solve Equation 1: [tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
- Subtract 11.3 from both sides:
[tex]\( 8.3 - 11.3 = -0.6x \)[/tex]
[tex]\( -3 = -0.6x \)[/tex]
- Divide by -0.6:
[tex]\( x = \frac{-3}{-0.6} = 5 \)[/tex]
### Solve Equation 2: [tex]\( 11.3 = 83 + 0.6x \)[/tex]
- Subtract 83 from both sides:
[tex]\( 11.3 - 83 = 0.6x \)[/tex]
[tex]\( -71.7 = 0.6x \)[/tex]
- Divide by 0.6:
[tex]\( x = \frac{-71.7}{0.6} = -119.5 \)[/tex]
### Solve Equation 3: [tex]\( 11.3 - 0.6x = 8.3 \)[/tex]
- Subtract 11.3 from both sides:
[tex]\( -0.6x = 8.3 - 11.3 \)[/tex]
[tex]\( -0.6x = -3 \)[/tex]
- Divide by -0.6:
[tex]\( x = \frac{-3}{-0.6} = 5 \)[/tex]
### Solve Equation 4: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
- Subtract 8.3 from both sides:
[tex]\( -0.6x = 11.3 - 8.3 \)[/tex]
[tex]\( -0.6x = 3 \)[/tex]
- Divide by -0.6:
[tex]\( x = \frac{3}{-0.6} = -5 \)[/tex]
After solving all four equations, we have the following solutions for [tex]\( x \)[/tex]:
- Equation 1: [tex]\( x = 5 \)[/tex]
- Equation 2: [tex]\( x = -119.5 \)[/tex]
- Equation 3: [tex]\( x = 5 \)[/tex]
- Equation 4: [tex]\( x = -5 \)[/tex]
The equation that gives a different value for [tex]\( x \)[/tex] compared to the other three is Equation 2, which results in [tex]\( x = -119.5 \)[/tex].
1. Equation 1: [tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
2. Equation 2: [tex]\( 11.3 = 83 + 0.6x \)[/tex]
3. Equation 3: [tex]\( 11.3 - 0.6x = 8.3 \)[/tex]
4. Equation 4: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
Now, let's solve each equation step by step.
### Solve Equation 1: [tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
- Subtract 11.3 from both sides:
[tex]\( 8.3 - 11.3 = -0.6x \)[/tex]
[tex]\( -3 = -0.6x \)[/tex]
- Divide by -0.6:
[tex]\( x = \frac{-3}{-0.6} = 5 \)[/tex]
### Solve Equation 2: [tex]\( 11.3 = 83 + 0.6x \)[/tex]
- Subtract 83 from both sides:
[tex]\( 11.3 - 83 = 0.6x \)[/tex]
[tex]\( -71.7 = 0.6x \)[/tex]
- Divide by 0.6:
[tex]\( x = \frac{-71.7}{0.6} = -119.5 \)[/tex]
### Solve Equation 3: [tex]\( 11.3 - 0.6x = 8.3 \)[/tex]
- Subtract 11.3 from both sides:
[tex]\( -0.6x = 8.3 - 11.3 \)[/tex]
[tex]\( -0.6x = -3 \)[/tex]
- Divide by -0.6:
[tex]\( x = \frac{-3}{-0.6} = 5 \)[/tex]
### Solve Equation 4: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
- Subtract 8.3 from both sides:
[tex]\( -0.6x = 11.3 - 8.3 \)[/tex]
[tex]\( -0.6x = 3 \)[/tex]
- Divide by -0.6:
[tex]\( x = \frac{3}{-0.6} = -5 \)[/tex]
After solving all four equations, we have the following solutions for [tex]\( x \)[/tex]:
- Equation 1: [tex]\( x = 5 \)[/tex]
- Equation 2: [tex]\( x = -119.5 \)[/tex]
- Equation 3: [tex]\( x = 5 \)[/tex]
- Equation 4: [tex]\( x = -5 \)[/tex]
The equation that gives a different value for [tex]\( x \)[/tex] compared to the other three is Equation 2, which results in [tex]\( x = -119.5 \)[/tex].
