Evaluate the expression when \( b=\frac{4}{7} \) and \( c=-\frac{5}{6} \) \[ 2 c-b \] Write your answer in simplest form. []
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Bonus Knowledge
To evaluate the expression \( 2c - b \) with \( b = \frac{4}{7} \) and \( c = -\frac{5}{6} \), we first need to calculate \( 2c \). Calculating \( 2c \): \[ 2c = 2 \left(-\frac{5}{6}\right) = -\frac{10}{6} = -\frac{5}{3} \] Now we substitute \( 2c \) and \( b \) into the expression: \[ 2c - b = -\frac{5}{3} - \frac{4}{7} \] Next, we need a common denominator to combine the fractions. The least common multiple of 3 and 7 is 21. Now, we rewrite each fraction with a denominator of 21: \[ -\frac{5}{3} = -\frac{5 \times 7}{3 \times 7} = -\frac{35}{21} \] \[ -\frac{4}{7} = -\frac{4 \times 3}{7 \times 3} = -\frac{12}{21} \] Now we can combine them: \[ 2c - b = -\frac{35}{21} - \frac{12}{21} = -\frac{35 + 12}{21} = -\frac{47}{21} \] Thus, the expression evaluated is: \[ \boxed{-\frac{47}{21}} \]