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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 determine which equation results in a different value of [tex]\( x \)[/tex], we need to solve each equation for [tex]\( x \)[/tex] and compare the results. Here’s how each equation is solved:

1. Equation 1:
[tex]\[
8.3 = -0.6x + 11.3
\][/tex]
- Subtract 11.3 from both sides:
[tex]\[
8.3 - 11.3 = -0.6x
\][/tex]
- Simplify the left side:
[tex]\[
-3 = -0.6x
\][/tex]
- Divide 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]
- Simplify:
[tex]\[
3 = 0.6x
\][/tex]
- Divide 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]
- Simplify:
[tex]\[
-0.6x = -3
\][/tex]
- Divide 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]
- Simplify:
[tex]\[
-0.6x = 3
\][/tex]
- Divide by -0.6 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{3}{-0.6} = -5
\][/tex]

Now, by comparing the solutions:
- Equations 1, 2, and 3 all yield [tex]\( x = 5 \)[/tex].
- Equation 4 yields [tex]\( x = -5 \)[/tex].

Therefore, the equation that results in a different value of [tex]\( x \)[/tex] is the fourth one:
[tex]\[ 8.3 - 0.6x = 11.3 \][/tex]

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