Question

Expand and simplify the expression: -5/7(3x + 1/4y) - 9(x/7 - 1/28y)
Fill in the blanks
(-5/7)(3x/1) + (-5/7)(1/4 ?) + (-9)(x/?) + (-9)(-1/28y)
-15x/7 - 5/28y - 9x/7 + ?/28y
-?/7x + 4/28y
-24/7x + ?/7y

Answer 1

Let's expand and simplify the expression step by step:

The original expression given is:
\[
-\frac{5}{7}(3x + \frac{1}{4}y) - 9\left(\frac{x}{7} - \frac{1}{28}y\right)
\]

**Step 1: Expand the first part**
\[
-\frac{5}{7}(3x) - \frac{5}{7}\left(\frac{1}{4}y\right) = -\frac{15}{7}x - \frac{5}{28}y
\]

**Step 2: Expand the second part**
\[
-9\left(\frac{x}{7}\right) + 9\left(\frac{1}{28}y\right) = -\frac{9}{7}x + \frac{9}{28}y
\]

**Step 3: Combine both parts**
Now, combine the two parts:
\[
-\frac{15}{7}x - \frac{5}{28}y - \frac{9}{7}x + \frac{9}{28}y
\]

**Step 4: Combine like terms**
For the \(x\) terms:
\[
-\frac{15}{7}x - \frac{9}{7}x = -\frac{24}{7}x
\]

For the \(y\) terms:
\[
-\frac{5}{28}y + \frac{9}{28}y = \frac{4}{28}y
\]

**Step 5: Putting it all together**
Thus, we have:
\[
-\frac{24}{7}x + \frac{4}{28}y
\]

**Step 6: Simplify \(\frac{4}{28}\) to \(\frac{1}{7}\)**
\[
\frac{4}{28}y = \frac{1}{7}y
\]

So, the final simplified expression is:
\[
-\frac{24}{7}x + \frac{1}{7}y
\]

Now, let's fill out the blanks:
- Expanding: \((-5/7)(3x/1) + (-5/7)(1/4y) + (-9)(x/7) + (-9)(-1/28y)\)
- We fill in: (-5/7)(3x/1) + (-5/7)(1/4y) + (-9)(x/7) + (-9)(-1/28y)

Which will lead to:
\[
- \frac{15}{7} x - \frac{5}{28} y - \frac{9}{7} x + \frac{9}{28} y
\]
- Combining terms for \(x\):
\(-\frac{15}{7} - \frac{9}{7} = -\frac{24}{7} x\)

- Combining terms for \(y\):
\(-\frac{5}{28} + \frac{9}{28} = \frac{4}{28} = \frac{1}{7}y\)

Therefore, the final expression in the form stated is:
\[
-\frac{24}{7}x + \frac{1}{7}y
\]

So, to fill in the final blanks:
- The values are:
1. -24 for the first blank,
2. 4 for the second blank,
3. 1 for the third blank.