To simplify the expression \( 7 \frac{3}{5}x - 4 \frac{1}{10}x + 8 \), we first convert the mixed numbers into improper fractions.
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Convert \( 7 \frac{3}{5} \) to improper fraction: \[ 7 \frac{3}{5} = \frac{7 \times 5 + 3}{5} = \frac{35 + 3}{5} = \frac{38}{5} \]
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Convert \( 4 \frac{1}{10} \) to improper fraction: \[ 4 \frac{1}{10} = \frac{4 \times 10 + 1}{10} = \frac{40 + 1}{10} = \frac{41}{10} \]
Now substitute these values into the original expression:
\[ \frac{38}{5}x - \frac{41}{10}x + 8 \]
Next, we need a common denominator to combine the \( x \) terms. The least common multiple of 5 and 10 is 10.
Convert \( \frac{38}{5}x \) to have a denominator of 10: \[ \frac{38}{5}x = \frac{38 \times 2}{5 \times 2}x = \frac{76}{10}x \]
Now substitute back into the expression: \[ \frac{76}{10}x - \frac{41}{10}x + 8 \]
Combine the \( x \) terms: \[ \left( \frac{76}{10} - \frac{41}{10} \right)x + 8 = \frac{35}{10}x + 8 \]
Now simplify \( \frac{35}{10} \): \[ \frac{35}{10} = \frac{7}{2} \]
Thus, the expression simplifies to: \[ \frac{7}{2}x + 8 \]
Putting it in the form specified in your original expression, we have: \[ [7] [2] / [1] x + [8] \]
In this case: \[ [7] [2] / [1] = \frac{7}{2}, \quad \text{and the constant part is } 8 \]
Therefore, the completed answer should be: \[ [7] [2] / [1] + [8] \]