College

Which equation, when solved, results in a different value of [tex]$x$[/tex] than the other three?

A. [tex]$8.3 = -0.6x + 11.3$[/tex]

B. [tex]$11.3 = 8.3 + 0.6x$[/tex]

C. [tex]$11.3 - 0.6x = 8.3$[/tex]

D. [tex]$8.3 - 0.6x = 11.3$[/tex]

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.