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.
