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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 :

To find out which equation results in a different value of [tex]\( x \)[/tex], let's solve each of them step by step.

1. Equation 1:
[tex]\( 8.3 = -0.6x + 11.3 \)[/tex]

- Start by isolating [tex]\( x \)[/tex]. Subtract 11.3 from both sides:
[tex]\[
8.3 - 11.3 = -0.6x
\][/tex]
[tex]\[
-3 = -0.6x
\][/tex]
- Divide both sides by -0.6:
[tex]\[
x = \frac{-3}{-0.6} = 5
\][/tex]

2. Equation 2:
[tex]\( 11.3 = 8.3 + 0.6x \)[/tex]

- Subtract 8.3 from both sides to isolate the terms with [tex]\( x \)[/tex]:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
[tex]\[
3 = 0.6x
\][/tex]
- Divide both sides by 0.6:
[tex]\[
x = \frac{3}{0.6} = 5
\][/tex]

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

- Subtract 8.3 from both sides:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
[tex]\[
3 = 0.6x
\][/tex]
- Divide both sides by 0.6:
[tex]\[
x = \frac{3}{0.6} = 5
\][/tex]

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

- Subtract 8.3 from both sides:
[tex]\[
-0.6x = 11.3 - 8.3
\][/tex]
[tex]\[
-0.6x = 3
\][/tex]
- Divide both sides by -0.6:
[tex]\[
x = \frac{3}{-0.6} = -5
\][/tex]

After solving all four equations, we can see that the value of [tex]\( x \)[/tex] is 5 for the first three equations and -5 for the fourth equation. Thus, the equation that results in a different value of [tex]\( x \)[/tex] is:

The fourth equation: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex]

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