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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]$11.3 = 8.3 + 0.8x$[/tex]

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

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

Answer :

Sure! Let's solve each of these equations one by one to determine which one results in a different value of [tex]\( x \)[/tex].

### Equation 1:
[tex]\[ 8.3 = -0.6x + 11.3 \][/tex]

To solve for [tex]\( x \)[/tex], let's move the terms around:
1. Subtract 11.3 from both sides:
[tex]\[ 8.3 - 11.3 = -0.6x \][/tex]
[tex]\[ -3.0 = -0.6x \][/tex]

2. Divide both sides by [tex]\(-0.6\)[/tex] to isolate [tex]\( x \)[/tex]:
[tex]\[ x = \frac{-3.0}{-0.6} \][/tex]
[tex]\[ x = 5 \][/tex]

### Equation 2:
[tex]\[ 11.3 = 8.3 + 0.8x \][/tex]

To solve for [tex]\( x \)[/tex]:
1. Subtract 8.3 from both sides:
[tex]\[ 11.3 - 8.3 = 0.8x \][/tex]
[tex]\[ 3.0 = 0.8x \][/tex]

2. Divide both sides by 0.8:
[tex]\[ x = \frac{3.0}{0.8} \][/tex]
[tex]\[ x = 3.75 \][/tex]

### Equation 3:
[tex]\[ 11.3 - 0.6x = 8.3 \][/tex]

To solve for [tex]\( x \)[/tex]:
1. Subtract 8.3 from both sides:
[tex]\[ 11.3 - 8.3 = 0.6x \][/tex]
[tex]\[ 3.0 = 0.6x \][/tex]

2. Divide both sides by 0.6:
[tex]\[ x = \frac{3.0}{0.6} \][/tex]
[tex]\[ x = 5 \][/tex]

### Equation 4:
[tex]\[ 8.3 - 0.6x = 11.3 \][/tex]

To solve for [tex]\( x \)[/tex]:
1. Subtract 8.3 from both sides:
[tex]\[ 8.3 - 11.3 = 0.6x \][/tex]
[tex]\[ -3.0 = 0.6x \][/tex]

2. Divide both sides by 0.6:
[tex]\[ x = \frac{-3.0}{0.6} \][/tex]
[tex]\[ x = -5 \][/tex]

### Conclusion
Now, let's compare the solutions:

- Equation 1: [tex]\( x = 5 \)[/tex]
- Equation 2: [tex]\( x = 3.75 \)[/tex]
- Equation 3: [tex]\( x = 5 \)[/tex]
- Equation 4: [tex]\( x = -5 \)[/tex]

The equation that results in a different value of [tex]\( x \)[/tex] from the others is Equation 2, which gives [tex]\( x = 3.75 \)[/tex], whereas the other equations yield either [tex]\( x = 5 \)[/tex] or [tex]\( x = -5 \)[/tex].

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