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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 :

Let's solve these equations one by one and determine which one gives a different result for [tex]\( x \)[/tex].

1. Equation 1:
[tex]\[
8.3 = -0.6x + 11.3
\][/tex]
To isolate [tex]\( x \)[/tex], first subtract 11.3 from both sides:
[tex]\[
8.3 - 11.3 = -0.6x
\][/tex]
Simplifying the left side, we get:
[tex]\[
-3 = -0.6x
\][/tex]
Divide both sides by -0.6 to solve for [tex]\( x \)[/tex]:
[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:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
Simplifying the left side, we get:
[tex]\[
3 = 0.6x
\][/tex]
Divide both sides by 0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{3}{0.6} = 5
\][/tex]

3. Equation 3:
[tex]\[
11.3 - 0.6x = 8.3
\][/tex]
Subtract 11.3 from both sides:
[tex]\[
-0.6x = 8.3 - 11.3
\][/tex]
Simplifying the right side, we get:
[tex]\[
-0.6x = -3
\][/tex]
Divide both sides by -0.6 to solve for [tex]\( x \)[/tex]:
[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]
Simplifying the right side, we get:
[tex]\[
-0.6x = 3
\][/tex]
Divide both sides by -0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{3}{-0.6} = -5
\][/tex]

In summary, the solutions for [tex]\( x \)[/tex] are:
- Equation 1: [tex]\( x = 5 \)[/tex]
- Equation 2: [tex]\( x = 5 \)[/tex]
- Equation 3: [tex]\( x = 5 \)[/tex]
- Equation 4: [tex]\( x = -5 \)[/tex]

The equation that results in a different value is Equation 4. Thus, Equation 4 is the one that gives a different solution for [tex]\( x \)[/tex] than the others.

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