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Answer :
To solve the question of which equation results in a different value of [tex]\(x\)[/tex], let's look at each equation individually and solve for [tex]\(x\)[/tex].
Equation A:
[tex]\[
8.3 = -0.6x + 11.3
\][/tex]
1. Subtract 11.3 from both sides:
[tex]\[
8.3 - 11.3 = -0.6x
\][/tex]
2. This simplifies to:
[tex]\[
-3 = -0.6x
\][/tex]
3. Divide both sides by -0.6 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{-3}{-0.6} = 5
\][/tex]
Equation B:
[tex]\[
11.3 = 8.3 + 0.6x
\][/tex]
1. Subtract 8.3 from both sides:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
2. This simplifies to:
[tex]\[
3 = 0.6x
\][/tex]
3. Divide both sides by 0.6 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{3}{0.6} = 5
\][/tex]
Equation C:
[tex]\[
11.3 - 0.6x = 8.3
\][/tex]
1. Subtract 11.3 from both sides:
[tex]\[
-0.6x = 8.3 - 11.3
\][/tex]
2. This simplifies to:
[tex]\[
-0.6x = -3
\][/tex]
3. Divide both sides by -0.6 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{-3}{-0.6} = 5
\][/tex]
Equation D:
[tex]\[
8.3 - 0.6x = 11.3
\][/tex]
1. Subtract 8.3 from both sides:
[tex]\[
-0.6x = 11.3 - 8.3
\][/tex]
2. This simplifies to:
[tex]\[
-0.6x = 3
\][/tex]
3. Divide both sides by -0.6 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{3}{-0.6} = -5
\][/tex]
After solving each equation, we find the solutions for [tex]\(x\)[/tex] are:
- Equation A: [tex]\(x = 5\)[/tex]
- Equation B: [tex]\(x = 5\)[/tex]
- Equation C: [tex]\(x = 5\)[/tex]
- Equation D: [tex]\(x = -5\)[/tex]
Thus, Equation D is the one that results in a different value of [tex]\(x\)[/tex] compared to the other three equations.
Equation A:
[tex]\[
8.3 = -0.6x + 11.3
\][/tex]
1. Subtract 11.3 from both sides:
[tex]\[
8.3 - 11.3 = -0.6x
\][/tex]
2. This simplifies to:
[tex]\[
-3 = -0.6x
\][/tex]
3. Divide both sides by -0.6 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{-3}{-0.6} = 5
\][/tex]
Equation B:
[tex]\[
11.3 = 8.3 + 0.6x
\][/tex]
1. Subtract 8.3 from both sides:
[tex]\[
11.3 - 8.3 = 0.6x
\][/tex]
2. This simplifies to:
[tex]\[
3 = 0.6x
\][/tex]
3. Divide both sides by 0.6 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{3}{0.6} = 5
\][/tex]
Equation C:
[tex]\[
11.3 - 0.6x = 8.3
\][/tex]
1. Subtract 11.3 from both sides:
[tex]\[
-0.6x = 8.3 - 11.3
\][/tex]
2. This simplifies to:
[tex]\[
-0.6x = -3
\][/tex]
3. Divide both sides by -0.6 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{-3}{-0.6} = 5
\][/tex]
Equation D:
[tex]\[
8.3 - 0.6x = 11.3
\][/tex]
1. Subtract 8.3 from both sides:
[tex]\[
-0.6x = 11.3 - 8.3
\][/tex]
2. This simplifies to:
[tex]\[
-0.6x = 3
\][/tex]
3. Divide both sides by -0.6 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{3}{-0.6} = -5
\][/tex]
After solving each equation, we find the solutions for [tex]\(x\)[/tex] are:
- Equation A: [tex]\(x = 5\)[/tex]
- Equation B: [tex]\(x = 5\)[/tex]
- Equation C: [tex]\(x = 5\)[/tex]
- Equation D: [tex]\(x = -5\)[/tex]
Thus, Equation D is the one that results in a different value of [tex]\(x\)[/tex] compared to the other three equations.
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