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Answer :
To determine which equation results in a different value of [tex]\( x \)[/tex] compared to the others, we can solve each equation step by step:
1. Solving the first equation
[tex]\[
8.3 = -0.6x + 11.3
\][/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. Solving the second equation
[tex]\[
11.3 = 8.3 + 0.6x
\][/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]
3. Solving the third equation
[tex]\[
11.3 - 0.6x = 8.3
\][/tex]
- Subtract 8.3 from both sides:
[tex]\[
11.3 - 8.3 - 0.6x = 0
\][/tex]
[tex]\[
3 - 0.6x = 0
\][/tex]
- Move 0.6x to the right side:
[tex]\[
3 = 0.6x
\][/tex]
- Divide both sides by 0.6:
[tex]\[
x = \frac{3}{0.6} = 5
\][/tex]
4. Solving the fourth equation
[tex]\[
8.3 - 0.6x = 11.3
\][/tex]
- Subtract 8.3 from both sides:
[tex]\[
8.3 - 11.3 - 0.6x = 0
\][/tex]
[tex]\[
-3 - 0.6x = 0
\][/tex]
- Move -3 to the right side:
[tex]\[
-0.6x = 3
\][/tex]
- Divide both sides by -0.6:
[tex]\[
x = \frac{3}{-0.6} = -5
\][/tex]
So, the solutions for each equation's [tex]\( x \)[/tex] are:
1. [tex]\( x = 5 \)[/tex]
2. [tex]\( x = 5 \)[/tex]
3. [tex]\( x = 5 \)[/tex]
4. [tex]\( x = -5 \)[/tex]
The fourth equation, [tex]\( 8.3 - 0.6x = 11.3 \)[/tex], results in a different value of [tex]\( x \)[/tex] from the other three. Therefore, this is the equation you are looking for.
1. Solving the first equation
[tex]\[
8.3 = -0.6x + 11.3
\][/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. Solving the second equation
[tex]\[
11.3 = 8.3 + 0.6x
\][/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]
3. Solving the third equation
[tex]\[
11.3 - 0.6x = 8.3
\][/tex]
- Subtract 8.3 from both sides:
[tex]\[
11.3 - 8.3 - 0.6x = 0
\][/tex]
[tex]\[
3 - 0.6x = 0
\][/tex]
- Move 0.6x to the right side:
[tex]\[
3 = 0.6x
\][/tex]
- Divide both sides by 0.6:
[tex]\[
x = \frac{3}{0.6} = 5
\][/tex]
4. Solving the fourth equation
[tex]\[
8.3 - 0.6x = 11.3
\][/tex]
- Subtract 8.3 from both sides:
[tex]\[
8.3 - 11.3 - 0.6x = 0
\][/tex]
[tex]\[
-3 - 0.6x = 0
\][/tex]
- Move -3 to the right side:
[tex]\[
-0.6x = 3
\][/tex]
- Divide both sides by -0.6:
[tex]\[
x = \frac{3}{-0.6} = -5
\][/tex]
So, the solutions for each equation's [tex]\( x \)[/tex] are:
1. [tex]\( x = 5 \)[/tex]
2. [tex]\( x = 5 \)[/tex]
3. [tex]\( x = 5 \)[/tex]
4. [tex]\( x = -5 \)[/tex]
The fourth equation, [tex]\( 8.3 - 0.6x = 11.3 \)[/tex], results in a different value of [tex]\( x \)[/tex] from the other three. Therefore, this is the equation you are looking for.
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