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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 + 0.6x[/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 equation step-by-step and determine which one yields a different value for [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]\[
-3.0 = -0.6x
\][/tex]

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

4. Simplify the fraction:
[tex]\[
x = 5
\][/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]\[
3.0 = 0.6x
\][/tex]

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

4. Simplify the fraction:
[tex]\[
x = 5
\][/tex]

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

1. Subtract 8.3 from both sides:
[tex]\[
11.3 - 0.6x - 8.3 = 0
\][/tex]

2. Simplify:
[tex]\[
3.0 - 0.6x = 0
\][/tex]

3. Subtract 3.0 from both sides:
[tex]\[
-0.6x = -3.0
\][/tex]

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

5. Simplify the fraction:
[tex]\[
x = 5
\][/tex]

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

1. Add 0.6x to both sides:
[tex]\[
8.3 = 11.3 + 0.6x
\][/tex]

2. Subtract 11.3 from both sides:
[tex]\[
8.3 - 11.3 = 0.6x
\][/tex]

3. Simplify:
[tex]\[
-3.0 = 0.6x
\][/tex]

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

5. Simplify the fraction:
[tex]\[
x = -5
\][/tex]

Now compare the results:

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

### Conclusion

The fourth equation, [tex]\( 8.3 - 0.6x = 11.3 \)[/tex], results in a different value of [tex]\( x \)[/tex] than the other three.

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