Answer :
To solve the problem, we need to determine which equation results in a different value of [tex]\( x \)[/tex] compared to the others. Let's go through each equation step-by-step to find their solutions.
### Equation 1:
[tex]\[ 8.3 = -0.6x + 11.3 \][/tex]
1. Subtract 11.3 from both sides:
[tex]\[ 8.3 - 11.3 = -0.6x \][/tex]
[tex]\[ -3 = -0.6x \][/tex]
2. Divide each side by -0.6:
[tex]\[ x = \frac{-3}{-0.6} \][/tex]
[tex]\[ x = 5 \][/tex]
### Equation 2:
[tex]\[ 11.3 = 8.3 + 0.6x \][/tex]
1. Subtract 8.3 from both sides:
[tex]\[ 11.3 - 8.3 = 0.6x \][/tex]
[tex]\[ 3 = 0.6x \][/tex]
2. Divide each side by 0.6:
[tex]\[ x = \frac{3}{0.6} \][/tex]
[tex]\[ x = 5 \][/tex]
### Equation 3:
[tex]\[ 11.3 - 0.6x = 8.3 \][/tex]
1. Subtract 11.3 from both sides:
[tex]\[ -0.6x = 8.3 - 11.3 \][/tex]
[tex]\[ -0.6x = -3 \][/tex]
2. Divide each side by -0.6:
[tex]\[ x = \frac{-3}{-0.6} \][/tex]
[tex]\[ x = 5 \][/tex]
### Equation 4:
[tex]\[ 8.3 - 0.6x = 11.3 \][/tex]
1. Subtract 8.3 from both sides:
[tex]\[ -0.6x = 11.3 - 8.3 \][/tex]
[tex]\[ -0.6x = 3 \][/tex]
2. Divide each side by -0.6:
[tex]\[ x = \frac{3}{-0.6} \][/tex]
[tex]\[ x = -5 \][/tex]
### Conclusion:
The solutions are:
- Equation 1 gives [tex]\( x = 5 \)[/tex].
- Equation 2 gives [tex]\( x = 5 \)[/tex].
- Equation 3 gives [tex]\( x = 5 \)[/tex].
- Equation 4 gives [tex]\( x = -5 \)[/tex].
The equation resulting in a different value of [tex]\( x \)[/tex] is Equation 4.
### Equation 1:
[tex]\[ 8.3 = -0.6x + 11.3 \][/tex]
1. Subtract 11.3 from both sides:
[tex]\[ 8.3 - 11.3 = -0.6x \][/tex]
[tex]\[ -3 = -0.6x \][/tex]
2. Divide each side by -0.6:
[tex]\[ x = \frac{-3}{-0.6} \][/tex]
[tex]\[ x = 5 \][/tex]
### Equation 2:
[tex]\[ 11.3 = 8.3 + 0.6x \][/tex]
1. Subtract 8.3 from both sides:
[tex]\[ 11.3 - 8.3 = 0.6x \][/tex]
[tex]\[ 3 = 0.6x \][/tex]
2. Divide each side by 0.6:
[tex]\[ x = \frac{3}{0.6} \][/tex]
[tex]\[ x = 5 \][/tex]
### Equation 3:
[tex]\[ 11.3 - 0.6x = 8.3 \][/tex]
1. Subtract 11.3 from both sides:
[tex]\[ -0.6x = 8.3 - 11.3 \][/tex]
[tex]\[ -0.6x = -3 \][/tex]
2. Divide each side by -0.6:
[tex]\[ x = \frac{-3}{-0.6} \][/tex]
[tex]\[ x = 5 \][/tex]
### Equation 4:
[tex]\[ 8.3 - 0.6x = 11.3 \][/tex]
1. Subtract 8.3 from both sides:
[tex]\[ -0.6x = 11.3 - 8.3 \][/tex]
[tex]\[ -0.6x = 3 \][/tex]
2. Divide each side by -0.6:
[tex]\[ x = \frac{3}{-0.6} \][/tex]
[tex]\[ x = -5 \][/tex]
### Conclusion:
The solutions are:
- Equation 1 gives [tex]\( x = 5 \)[/tex].
- Equation 2 gives [tex]\( x = 5 \)[/tex].
- Equation 3 gives [tex]\( x = 5 \)[/tex].
- Equation 4 gives [tex]\( x = -5 \)[/tex].
The equation resulting in a different value of [tex]\( x \)[/tex] is Equation 4.
