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 solve each equation one by one:
### Equation A:
[tex]\[ 8.3 = -0.6x + 11.3 \][/tex]
1. Subtract 11.3 from both sides to isolate terms with [tex]\( x \)[/tex]:
[tex]\[ 8.3 - 11.3 = -0.6x \][/tex]
2. Simplify:
[tex]\[ -3 = -0.6x \][/tex]
3. Divide both sides by -0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{-3}{-0.6} = 5 \][/tex]
### Equation B:
[tex]\[ 11.3 = 8.3 + 0.6x \][/tex]
1. Subtract 8.3 from both sides:
[tex]\[ 11.3 - 8.3 = 0.6x \][/tex]
2. Simplify:
[tex]\[ 3 = 0.6x \][/tex]
3. Divide by 0.6:
[tex]\[ x = \frac{3}{0.6} = 5 \][/tex]
### Equation C:
[tex]\[ 11.3 - 0.6x = 8.3 \][/tex]
1. Subtract 11.3 from both sides:
[tex]\[ -0.6x = 8.3 - 11.3 \][/tex]
2. Simplify:
[tex]\[ -0.6x = -3 \][/tex]
3. Divide by -0.6:
[tex]\[ x = \frac{-3}{-0.6} = 5 \][/tex]
### Equation D:
[tex]\[ 8.3 - 0.6x = 11.3 \][/tex]
1. Subtract 8.3 from both sides:
[tex]\[ -0.6x = 11.3 - 8.3 \][/tex]
2. Simplify:
[tex]\[ -0.6x = 3 \][/tex]
3. Divide by -0.6:
[tex]\[ x = \frac{3}{-0.6} = -5 \][/tex]
Now that we have solved all the equations, we can see the solutions are:
- Equation A gives [tex]\( x = 5 \)[/tex]
- Equation B gives [tex]\( x = 5 \)[/tex]
- Equation C gives [tex]\( x = 5 \)[/tex]
- Equation D gives [tex]\( x = -5 \)[/tex]
The equation that results in a different value of [tex]\( x \)[/tex] is Equation D.
### Equation A:
[tex]\[ 8.3 = -0.6x + 11.3 \][/tex]
1. Subtract 11.3 from both sides to isolate terms with [tex]\( x \)[/tex]:
[tex]\[ 8.3 - 11.3 = -0.6x \][/tex]
2. Simplify:
[tex]\[ -3 = -0.6x \][/tex]
3. Divide both sides by -0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{-3}{-0.6} = 5 \][/tex]
### Equation B:
[tex]\[ 11.3 = 8.3 + 0.6x \][/tex]
1. Subtract 8.3 from both sides:
[tex]\[ 11.3 - 8.3 = 0.6x \][/tex]
2. Simplify:
[tex]\[ 3 = 0.6x \][/tex]
3. Divide by 0.6:
[tex]\[ x = \frac{3}{0.6} = 5 \][/tex]
### Equation C:
[tex]\[ 11.3 - 0.6x = 8.3 \][/tex]
1. Subtract 11.3 from both sides:
[tex]\[ -0.6x = 8.3 - 11.3 \][/tex]
2. Simplify:
[tex]\[ -0.6x = -3 \][/tex]
3. Divide by -0.6:
[tex]\[ x = \frac{-3}{-0.6} = 5 \][/tex]
### Equation D:
[tex]\[ 8.3 - 0.6x = 11.3 \][/tex]
1. Subtract 8.3 from both sides:
[tex]\[ -0.6x = 11.3 - 8.3 \][/tex]
2. Simplify:
[tex]\[ -0.6x = 3 \][/tex]
3. Divide by -0.6:
[tex]\[ x = \frac{3}{-0.6} = -5 \][/tex]
Now that we have solved all the equations, we can see the solutions are:
- Equation A gives [tex]\( x = 5 \)[/tex]
- Equation B gives [tex]\( x = 5 \)[/tex]
- Equation C gives [tex]\( x = 5 \)[/tex]
- Equation D gives [tex]\( x = -5 \)[/tex]
The equation that results in a different value of [tex]\( x \)[/tex] is Equation D.
