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Answer :
Let's solve each equation step by step.
[tex]$$\textbf{Equation A: } 8.3 = -0.6x + 11.3$$[/tex]
1. Subtract [tex]\(11.3\)[/tex] from both sides:
[tex]$$8.3 - 11.3 = -0.6x$$[/tex]
[tex]$$-3 = -0.6x$$[/tex]
2. Divide both sides by [tex]\(-0.6\)[/tex]:
[tex]$$x = \frac{-3}{-0.6} = 5.$$[/tex]
---
[tex]$$\textbf{Equation B: } 11.3 = 8.3 + 0.6x$$[/tex]
1. Subtract [tex]\(8.3\)[/tex] from both sides:
[tex]$$11.3 - 8.3 = 0.6x$$[/tex]
[tex]$$3 = 0.6x$$[/tex]
2. Divide both sides by [tex]\(0.6\)[/tex]:
[tex]$$x = \frac{3}{0.6} = 5.$$[/tex]
---
[tex]$$\textbf{Equation C: } 11.3 - 0.6x = 8.3$$[/tex]
1. Subtract [tex]\(11.3\)[/tex] from both sides:
[tex]$$-0.6x = 8.3 - 11.3$$[/tex]
[tex]$$-0.6x = -3$$[/tex]
2. Divide both sides by [tex]\(-0.6\)[/tex]:
[tex]$$x = \frac{-3}{-0.6} = 5.$$[/tex]
---
[tex]$$\textbf{Equation D: } 8.3 - 0.6x = 11.3$$[/tex]
1. Subtract [tex]\(8.3\)[/tex] from both sides:
[tex]$$-0.6x = 11.3 - 8.3$$[/tex]
[tex]$$-0.6x = 3$$[/tex]
2. Divide both sides by [tex]\(-0.6\)[/tex]:
[tex]$$x = \frac{3}{-0.6} = -5.$$[/tex]
---
Comparing the solutions:
- Equations A, B, and C all give [tex]\(x = 5\)[/tex].
- Equation D gives [tex]\(x = -5\)[/tex].
Thus, the equation that results in a different value of [tex]\(x\)[/tex] is:
[tex]$$\boxed{8.3 - 0.6x = 11.3}.$$[/tex]
[tex]$$\textbf{Equation A: } 8.3 = -0.6x + 11.3$$[/tex]
1. Subtract [tex]\(11.3\)[/tex] from both sides:
[tex]$$8.3 - 11.3 = -0.6x$$[/tex]
[tex]$$-3 = -0.6x$$[/tex]
2. Divide both sides by [tex]\(-0.6\)[/tex]:
[tex]$$x = \frac{-3}{-0.6} = 5.$$[/tex]
---
[tex]$$\textbf{Equation B: } 11.3 = 8.3 + 0.6x$$[/tex]
1. Subtract [tex]\(8.3\)[/tex] from both sides:
[tex]$$11.3 - 8.3 = 0.6x$$[/tex]
[tex]$$3 = 0.6x$$[/tex]
2. Divide both sides by [tex]\(0.6\)[/tex]:
[tex]$$x = \frac{3}{0.6} = 5.$$[/tex]
---
[tex]$$\textbf{Equation C: } 11.3 - 0.6x = 8.3$$[/tex]
1. Subtract [tex]\(11.3\)[/tex] from both sides:
[tex]$$-0.6x = 8.3 - 11.3$$[/tex]
[tex]$$-0.6x = -3$$[/tex]
2. Divide both sides by [tex]\(-0.6\)[/tex]:
[tex]$$x = \frac{-3}{-0.6} = 5.$$[/tex]
---
[tex]$$\textbf{Equation D: } 8.3 - 0.6x = 11.3$$[/tex]
1. Subtract [tex]\(8.3\)[/tex] from both sides:
[tex]$$-0.6x = 11.3 - 8.3$$[/tex]
[tex]$$-0.6x = 3$$[/tex]
2. Divide both sides by [tex]\(-0.6\)[/tex]:
[tex]$$x = \frac{3}{-0.6} = -5.$$[/tex]
---
Comparing the solutions:
- Equations A, B, and C all give [tex]\(x = 5\)[/tex].
- Equation D gives [tex]\(x = -5\)[/tex].
Thus, the equation that results in a different value of [tex]\(x\)[/tex] is:
[tex]$$\boxed{8.3 - 0.6x = 11.3}.$$[/tex]
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