High School

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] than the others, we need to solve each equation for [tex]\( x \)[/tex]. Let's go through them one by one:

1. Equation: [tex]\( 8.3 = -0.6x + 11.3 \)[/tex]
- Rearrange to solve for [tex]\( x \)[/tex]:
[tex]\[
8.3 - 11.3 = -0.6x
\][/tex]
[tex]\[
-3 = -0.6x
\][/tex]
[tex]\[
x = \frac{-3}{-0.6} = 5
\][/tex]

2. Equation: [tex]\( 11.3 = 8.3 + 0.6x \)[/tex]
- Rearrange to solve for [tex]\( x \)[/tex]:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
[tex]\[
3 = 0.6x
\][/tex]
[tex]\[
x = \frac{3}{0.6} = 5
\][/tex]

3. Equation: [tex]\( 11.3 - 0.6x = 8.3 \)[/tex]
- Rearrange to solve for [tex]\( x \)[/tex]:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
[tex]\[
3 = 0.6x
\][/tex]
[tex]\[
x = \frac{3}{0.6} = 5
\][/tex]

4. Equation: [tex]\( 8.3 - 0.6x = 11.3 \)[/tex]
- Rearrange to solve for [tex]\( x \)[/tex]:
[tex]\[
8.3 - 11.3 = 0.6x
\][/tex]
[tex]\[
-3 = 0.6x
\][/tex]
[tex]\[
x = \frac{-3}{0.6} = -5
\][/tex]

Based on the solutions we found:

- The first three equations all result in [tex]\( x = 5 \)[/tex].
- The fourth equation results in [tex]\( x = -5 \)[/tex].

Thus, the equation that results in a different value of [tex]\( x \)[/tex] than the other three is:

[tex]\( 8.3 - 0.6x = 11.3 \)[/tex], which gives [tex]\( x = -5 \)[/tex].

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