Answered

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Solve the equation:

[tex]\(\frac{5}{6}c - 1 = 1 + \frac{5}{6}c\)[/tex]

A. Infinite solutions
B. No solution
C. [tex]\(c = \frac{5}{6}\)[/tex]
D. [tex]\(c = \frac{12}{10}\)[/tex]

Sagot :

GinnyAnswer
Let's solve the equation step-by-step to determine the correct answer:

We start with the given equation:

[tex]\[ \frac{5}{6} c - 1 = 1 + \frac{5}{6} c \][/tex]

1. Subtract [tex]\(\frac{5}{6} c\)[/tex] from both sides of the equation to attempt isolating [tex]\(c\)[/tex]:

[tex]\[ \frac{5}{6} c - 1 - \frac{5}{6} c = 1 + \frac{5}{6} c - \frac{5}{6} c \][/tex]

This simplifies to:

[tex]\[ -1 = 1 \][/tex]

2. We recognize that this simplification leads to a contradiction. The statement [tex]\(-1 = 1\)[/tex] is clearly false and never true.

Given this contradiction, we can conclude that there is no possible value for [tex]\(c\)[/tex] that would satisfy the original equation. Hence, the equation has:

[tex]\[ \boxed{\text{No solution}} \][/tex]

This means that the equation is inconsistent and there is no value of [tex]\(c\)[/tex] that will make the left side equal to the right side.
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