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Evaluate the expression when \( b=\frac{4}{7} \) and \( c=-\frac{5}{6} \) \[ 2 c-b \] Write your answer in simplest form. []

Ask by Mccoy Bernard. in the United States
Feb 21,2025

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Answer

The expression \( 2c - b \) evaluates to \( -\frac{47}{21} \) when \( b=\frac{4}{7} \) and \( c=-\frac{5}{6} \).

Solution

Substitute \( b=\frac{4}{7} \) and \( c=-\frac{5}{6} \) into the expression \( 2c-b \). Evaluate the expression by following steps: - step0: Evaluate: \(2c-b\) - step1: Substitute: \(2\left(-\frac{5}{6}\right)-\frac{4}{7}\) - step2: Multiply the numbers: \(-\frac{5}{3}-\frac{4}{7}\) - step3: Reduce fractions to a common denominator: \(-\frac{5\times 7}{3\times 7}-\frac{4\times 3}{7\times 3}\) - step4: Multiply the numbers: \(-\frac{5\times 7}{21}-\frac{4\times 3}{7\times 3}\) - step5: Multiply the numbers: \(-\frac{5\times 7}{21}-\frac{4\times 3}{21}\) - step6: Transform the expression: \(\frac{-5\times 7-4\times 3}{21}\) - step7: Multiply the numbers: \(\frac{-35-4\times 3}{21}\) - step8: Multiply the numbers: \(\frac{-35-12}{21}\) - step9: Subtract the numbers: \(\frac{-47}{21}\) - step10: Rewrite the fraction: \(-\frac{47}{21}\) When \( b=\frac{4}{7} \) and \( c=-\frac{5}{6} \), the expression \( 2c-b \) simplifies to \( -\frac{47}{21} \) or \( -2\frac{5}{21} \) or \( -2.238095 \) in simplest form.

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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: \[ \boxed{-\frac{47}{21}} \]

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