Answer :
To determine which equation results in a different value of [tex]\( x \)[/tex], we need to solve each equation and find the value of [tex]\( x \)[/tex].
### 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]
2. Simplify:
[tex]\[ -3 = -0.6x \][/tex]
3. Divide by [tex]\(-0.6\)[/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:
[tex]\[ 11.3 - 8.3 = 0.6x \][/tex]
2. Simplify:
[tex]\[ 3 = 0.6x \][/tex]
3. Divide by 0.6:
[tex]\[ x = \frac{3}{0.6} = 5.0 \][/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]
2. Simplify:
[tex]\[ -0.6x = -3 \][/tex]
3. Divide by [tex]\(-0.6\)[/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:
[tex]\[ -0.6x = 11.3 - 8.3 \][/tex]
2. Simplify:
[tex]\[ -0.6x = 3 \][/tex]
3. Divide by [tex]\(-0.6\)[/tex]:
[tex]\[ x = \frac{3}{-0.6} = -5.0 \][/tex]
### Conclusion:
Equations 1, 2, and 3 all result in an [tex]\( x \)[/tex] value of 5.0. However, Equation 4 gives an [tex]\( x \)[/tex] value of [tex]\(-5.0\)[/tex]. Therefore, the equation that results 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]
2. Simplify:
[tex]\[ -3 = -0.6x \][/tex]
3. Divide by [tex]\(-0.6\)[/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:
[tex]\[ 11.3 - 8.3 = 0.6x \][/tex]
2. Simplify:
[tex]\[ 3 = 0.6x \][/tex]
3. Divide by 0.6:
[tex]\[ x = \frac{3}{0.6} = 5.0 \][/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]
2. Simplify:
[tex]\[ -0.6x = -3 \][/tex]
3. Divide by [tex]\(-0.6\)[/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:
[tex]\[ -0.6x = 11.3 - 8.3 \][/tex]
2. Simplify:
[tex]\[ -0.6x = 3 \][/tex]
3. Divide by [tex]\(-0.6\)[/tex]:
[tex]\[ x = \frac{3}{-0.6} = -5.0 \][/tex]
### Conclusion:
Equations 1, 2, and 3 all result in an [tex]\( x \)[/tex] value of 5.0. However, Equation 4 gives an [tex]\( x \)[/tex] value of [tex]\(-5.0\)[/tex]. Therefore, the equation that results in a different value of [tex]\( x \)[/tex] is Equation 4.
