Let's simplify each expression step by step:
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For the expression \(4b + 3c - 2b + 7c\):
- Combine like terms for \(b\): \(4b - 2b = 2b\)
- Combine like terms for \(c\): \(3c + 7c = 10c\)
- Thus, the expression simplifies to: \[ 2b + 10c \]
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For the expression \(\frac{4}{6}x + \frac{10}{15}y\):
- Simplify \(\frac{4}{6}\) and \(\frac{10}{15}\): \(\frac{4}{6} = \frac{2}{3}\) and \(\frac{10}{15} = \frac{2}{3}\)
- So, the expression becomes: \[ \frac{2}{3}x + \frac{2}{3}y \]
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For the expression \(\frac{1}{2}x + 1 \frac{3}{10}y\):
- Convert the mixed number to an improper fraction: \(1 \frac{3}{10} = \frac{10}{10} + \frac{3}{10} = \frac{13}{10}\)
- The expression is now: \[ \frac{1}{2}x + \frac{13}{10}y \]
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For the expression \(\frac{1}{4}x + \frac{13}{10}y\), it is already simplified.
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For the expression \(1 \frac{1}{4}x + 1y\):
- Convert the mixed number to an improper fraction: \(1 \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4}\)
- So the expression can be written as: \[ \frac{5}{4}x + 1y \quad \text{or just} \quad \frac{5}{4}x + y \]
In summary, the simplified expressions are:
- \(2b + 10c\)
- \(\frac{2}{3}x + \frac{2}{3}y\)
- \(\frac{1}{2}x + \frac{13}{10}y\)
- \(\frac{1}{4}x + \frac{13}{10}y\) (already simplified)
- \(\frac{5}{4}x + y\)