Question

Fill in the blanks!
Expand and simplify the expression:

-5/7 (3x + 1/4y) - 9 (x/7 - 1/28 y)
(-5/7)(3x/1) + (-5/7)(1/4 _) + (-9) (x/_) + (-9) (-1/28y)
-15x/7 - 5/28 y - 9x/7 + _/28 y
- _/7 x + 4/28 y
-24/7 x + _/7 y

Answer 1

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

1. Expand \(-\frac{5}{7} (3x)\):
\[
-\frac{5}{7} \cdot 3x = -\frac{15}{7}x
\]

2. Expand \(-\frac{5}{7} \left(\frac{1}{4}y\right)\):
\[
-\frac{5}{7} \cdot \frac{1}{4}y = -\frac{5}{28}y
\]

3. Expand \(-9\left(\frac{x}{7}\right)\):
\[
-9 \cdot \frac{x}{7} = -\frac{9}{7}x
\]

4. 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

1. Combine the \(x\) terms:
\[
-\frac{15}{7}x - \frac{9}{7}x = -\left(\frac{15 + 9}{7}\right)x = -\frac{24}{7}x
\]

2. 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:

1. First line expansion:
- (-5/7)(3x/1) + (-5/7)(1/4 **y**) + (-9) (**7**) + (-9) (-1/28y)

2. After gathering like terms:
- - **24/7** x + **1/7** y

Thus, the filled blanks are:

\[
-5/7 (3x + 1/4y) - 9 (x/7 - 1/28 y)
\]
\[
(-5/7)(3x) + (-5/7)(1/4 y) + (-9) (x/7) + (-9) (-1/28y)
\]
\[
-15/7 x - 5/28 y - 9/7 x + 9/28 y
\]
\[
- 24/7 x + 4/28 y
\]
\[
-24/7 x + 1/7 y
\]