To expand the expression \( \frac{7}{10}(5d + 6) \), you need to distribute \( \frac{7}{10} \) to both terms inside the parentheses.
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Distributing \( \frac{7}{10} \) to \( 5d \): \[ \frac{7}{10} \times 5d = \frac{35d}{10} = 3.5d \quad \text{or} \quad 35d/10 \]
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Distributing \( \frac{7}{10} \) to \( 6 \): \[ \frac{7}{10} \times 6 = \frac{42}{10} = 4.2 \quad \text{or} \quad 42/10 \]
Combining these, we get: \[ \frac{7}{10}(5d + 6) = 3.5d + 4.2 \]
Expressing it in fractional form (if necessary): \[ = \frac{35d}{10} + \frac{42}{10} = \frac{35d + 42}{10} \]
However, if we keep it in simpler terms, it results in: \[ 35d + 42 \]
So, the expanded form of \( \frac{7}{10}(5d + 6) \) is: \[ \boxed{35d + 42} \]