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Answer :
Let's solve each of the four equations individually to see which one gives a different solution for [tex]\( x \)[/tex].
### Equation 1:
[tex]\[ 8.3 = -0.6x + 11.3 \][/tex]
1. Subtract 11.3 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ 8.3 - 11.3 = -0.6x \][/tex]
2. Simplify the left side:
[tex]\[ -3 = -0.6x \][/tex]
3. Divide both sides by [tex]\(-0.6\)[/tex] to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{-3}{-0.6} = 5.0 \][/tex]
### Equation 2:
[tex]\[ 11.3 = 8.3 + 0.6x \][/tex]
1. Subtract 8.3 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ 11.3 - 8.3 = 0.6x \][/tex]
2. Simplify the left side:
[tex]\[ 3 = 0.6x \][/tex]
3. Divide both sides by 0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{3}{0.6} = 5.0 \][/tex]
### Equation 3:
[tex]\[ 11.3 - 0.6x = 8.3 \][/tex]
1. Subtract 11.3 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ -0.6x = 8.3 - 11.3 \][/tex]
2. Simplify the right side:
[tex]\[ -0.6x = -3 \][/tex]
3. Divide both sides by [tex]\(-0.6\)[/tex] to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{-3}{-0.6} = 5.0 \][/tex]
### Equation 4:
[tex]\[ 8.3 - 0.6x = 11.3 \][/tex]
1. Subtract 8.3 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ -0.6x = 11.3 - 8.3 \][/tex]
2. Simplify the right side:
[tex]\[ -0.6x = 3 \][/tex]
3. Divide both sides by [tex]\(-0.6\)[/tex] to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{3}{-0.6} = -5.0 \][/tex]
### Conclusion
The solutions for the equations are:
- Equation 1: [tex]\( x = 5.0 \)[/tex]
- Equation 2: [tex]\( x = 5.0 \)[/tex]
- Equation 3: [tex]\( x = 5.0 \)[/tex]
- Equation 4: [tex]\( x = -5.0 \)[/tex]
Equation 4 results in a different value for [tex]\( x \)[/tex] compared to the other three equations.
### Equation 1:
[tex]\[ 8.3 = -0.6x + 11.3 \][/tex]
1. Subtract 11.3 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ 8.3 - 11.3 = -0.6x \][/tex]
2. Simplify the left side:
[tex]\[ -3 = -0.6x \][/tex]
3. Divide both sides by [tex]\(-0.6\)[/tex] to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{-3}{-0.6} = 5.0 \][/tex]
### Equation 2:
[tex]\[ 11.3 = 8.3 + 0.6x \][/tex]
1. Subtract 8.3 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ 11.3 - 8.3 = 0.6x \][/tex]
2. Simplify the left side:
[tex]\[ 3 = 0.6x \][/tex]
3. Divide both sides by 0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{3}{0.6} = 5.0 \][/tex]
### Equation 3:
[tex]\[ 11.3 - 0.6x = 8.3 \][/tex]
1. Subtract 11.3 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ -0.6x = 8.3 - 11.3 \][/tex]
2. Simplify the right side:
[tex]\[ -0.6x = -3 \][/tex]
3. Divide both sides by [tex]\(-0.6\)[/tex] to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{-3}{-0.6} = 5.0 \][/tex]
### Equation 4:
[tex]\[ 8.3 - 0.6x = 11.3 \][/tex]
1. Subtract 8.3 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ -0.6x = 11.3 - 8.3 \][/tex]
2. Simplify the right side:
[tex]\[ -0.6x = 3 \][/tex]
3. Divide both sides by [tex]\(-0.6\)[/tex] to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{3}{-0.6} = -5.0 \][/tex]
### Conclusion
The solutions for the equations are:
- Equation 1: [tex]\( x = 5.0 \)[/tex]
- Equation 2: [tex]\( x = 5.0 \)[/tex]
- Equation 3: [tex]\( x = 5.0 \)[/tex]
- Equation 4: [tex]\( x = -5.0 \)[/tex]
Equation 4 results in a different value for [tex]\( x \)[/tex] compared to the other three equations.
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