Let's start filling in the blanks step by step!
We need to expand and simplify the following expression:
\[
- \frac{5}{7}(3x + \frac{1}{4}y) - 9\left(\frac{x}{7} - \frac{1}{28}y\right) \]
Step 1: Expand the expression
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Expand \(-\frac{5}{7} (3x)\): \[ -\frac{5}{7} \cdot 3x = -\frac{15}{7}x \]
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Expand \(-\frac{5}{7} \left(\frac{1}{4}y\right)\): \[ -\frac{5}{7} \cdot \frac{1}{4}y = -\frac{5}{28}y \]
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Expand \(-9\left(\frac{x}{7}\right)\): \[ -9 \cdot \frac{x}{7} = -\frac{9}{7}x \]
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Expand \(-9\left(-\frac{1}{28}y\right)\): \[ -9 \cdot \left(-\frac{1}{28}y\right) = \frac{9}{28}y \]
Step 2: Combine all these parts together
Putting these expressions together, we have: \[ -\frac{15}{7}x - \frac{5}{28}y - \frac{9}{7}x + \frac{9}{28}y \]
Step 3: Combine like terms
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Combine the \(x\) terms: \[ -\frac{15}{7}x - \frac{9}{7}x = -\left(\frac{15 + 9}{7}\right)x = -\frac{24}{7}x \]
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Combine the \(y\) terms: \[ -\frac{5}{28}y + \frac{9}{28}y = \left(-5 + 9\right) \frac{1}{28}y = \frac{4}{28}y = \frac{1}{7}y \]
Final Expression
Putting it all together, we get: \[ -\frac{24}{7}x + \frac{1}{7}y \]
Now we fill the blanks based on our calculations:
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First line expansion:
- (-5/7)(3x/1) + (-5/7)(1/4 y) + (-9) (7) + (-9) (-1/28y)
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After gathering like terms:
-
- 24/7 x + 1/7 y
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Thus, the filled blanks are:
\[ -5/7 (3x + 1/4y) - 9 (x/7 - 1/28 y) \] \[ (-5/7)(3x) + (-5/7)(1/4 y) + (-9) (x/7) + (-9) (-1/28y) \] \[ -15/7 x - 5/28 y - 9/7 x + 9/28 y \] \[
- 24/7 x + 4/28 y \] \[ -24/7 x + 1/7 y \]