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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 - 0.8x + 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 - 0.8x = 11.3[/tex]

Answer :

We start by solving each equation for [tex]\( x \)[/tex].

1. Equation 1:
The equation is
[tex]\[
8.3 - (-0.8x) = 11.3.
\][/tex]
Simplify the left-hand side by changing the double negative:
[tex]\[
8.3 + 0.8x = 11.3.
\][/tex]
Subtract [tex]\( 8.3 \)[/tex] from both sides:
[tex]\[
0.8x = 11.3 - 8.3 = 3.0.
\][/tex]
Divide both sides by [tex]\( 0.8 \)[/tex]:
[tex]\[
x = \frac{3.0}{0.8} = 3.75.
\][/tex]

2. Equation 2:
The equation is
[tex]\[
11.3 = 8.3 + 0.6x.
\][/tex]
Subtract [tex]\( 8.3 \)[/tex] from both sides:
[tex]\[
0.6x = 11.3 - 8.3 = 3.0.
\][/tex]
Divide both sides by [tex]\( 0.6 \)[/tex]:
[tex]\[
x = \frac{3.0}{0.6} = 5.0.
\][/tex]

3. Equation 3:
The equation is
[tex]\[
11.3 - 0.6x = 8.3.
\][/tex]
Subtract [tex]\( 11.3 \)[/tex] from both sides:
[tex]\[
-0.6x = 8.3 - 11.3 = -3.0.
\][/tex]
Divide both sides by [tex]\( -0.6 \)[/tex]:
[tex]\[
x = \frac{-3.0}{-0.6} = 5.0.
\][/tex]

4. Equation 4:
The equation is
[tex]\[
8.3 - 0.8x = 11.3.
\][/tex]
Subtract [tex]\( 8.3 \)[/tex] from both sides:
[tex]\[
-0.8x = 11.3 - 8.3 = 3.0.
\][/tex]
Divide both sides by [tex]\( -0.8 \)[/tex]:
[tex]\[
x = \frac{3.0}{-0.8} = -3.75.
\][/tex]

Now, comparing the solutions:

- Equation 1 gives [tex]\( x = 3.75 \)[/tex].
- Equation 2 gives [tex]\( x = 5.0 \)[/tex].
- Equation 3 gives [tex]\( x = 5.0 \)[/tex].
- Equation 4 gives [tex]\( x = -3.75 \)[/tex].

Notice that two of the equations (Equations 2 and 3) yield [tex]\( x = 5.0 \)[/tex]. Since the majority value is [tex]\( 5.0 \)[/tex], the equation that produces a different value is Equation 4, where [tex]\( x = -3.75 \)[/tex].

Thus, the equation with the different value of [tex]\( x \)[/tex] is Equation 4.

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