Question
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\( \frac{5 x-15}{35}+\frac{7 x-21}{5}=\square \) (Simplify your answer. Use integers or fractions for any numbers in the expression.)

Ask by Wang Mccarthy. in the United States
Jan 21,2025

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Answer

The simplified expression is \( \frac{54x-162}{35} \).

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Bonus Knowledge

To solve the equation \( \frac{5 x-15}{35}+\frac{7 x-21}{5}=\square \), we first simplify each term. The first term can be simplified as follows: \[ \frac{5(x - 3)}{35} = \frac{x - 3}{7} \] The second term: \[ \frac{7(x - 3)}{5} = \frac{7x - 21}{5} \] Now the equation becomes: \[ \frac{x - 3}{7} + \frac{7(x - 3)}{5} \] Next, we find a common denominator for the two fractions. The common denominator of 7 and 5 is 35. Therefore, we rewrite the equation: \[ \frac{5(x - 3)}{35} + \frac{49(x - 3)}{35} \] Combining the fractions gives: \[ \frac{5(x - 3) + 49(x - 3)}{35} = \frac{(5 + 49)(x - 3)}{35} = \frac{54(x - 3)}{35} \] Thus, the simplified form is: \[ \frac{54(x - 3)}{35} \] Now, for any expression, we can substitute specific values for \( x \) to evaluate further, or leave it in this simplified form. The answer for \( \square \) is: \[ \frac{54(x - 3)}{35} \]

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