Question

Fill in the blanks!

Expand and simplify the expression:
-5/7 (3x + 1/4y) + 9 (x/7 - 1/28y)

1. Use the distributive property to expand each expression.
(-5/7) (_) + (-5/7) (1/4y) + 9 (x/_) -9 (1/28y)

2. Combine like terms.
-15x/7 - _/28 y + 9x/7 - _/28y
-6x/7 - 14/28 y
-6x/7 - _/2 y

Answer 1

Let's fill in the blanks step by step.

1. **Use the distributive property to expand each expression.**

The expression to expand is:
\[
-5/7 (3x + 1/4y) + 9 (x/7 - 1/28y)
\]

Expanding the first part:
\[
-5/7 (3x) + (-5/7)(1/4y) = -\frac{15x}{7} - \frac{5}{28}y
\]

Expanding the second part:
\[
9 (x/7) - 9 (1/28y) = \frac{9x}{7} - \frac{9}{28}y
\]

So we have:
\[
-\frac{15x}{7} - \frac{5}{28}y + \frac{9x}{7} - \frac{9}{28}y
\]

The filled-in statement is:
\[
(-5/7) (3x) + (-5/7) (1/4y) + 9 (x/7) - 9 (1/28y)
\]

2. **Combine like terms.**

Collecting like terms for \(x\):
\[
-\frac{15x}{7} + \frac{9x}{7} = \frac{-15x + 9x}{7} = \frac{-6x}{7}
\]

Now, for \(y\):
\[
-\frac{5}{28}y - \frac{9}{28}y = \frac{-5y - 9y}{28} = \frac{-14y}{28} = -\frac{1}{2}y
\]

Now putting it all together, we get:
\[
-\frac{6x}{7} - \frac{1}{2}y
\]

So the filled-in statements for the simplified expression are:
1. **Fill-in for the first part:** \((-5/7) (3x) + (-5/7) (1/4y) + 9 (x/7) - 9 (1/28y)\)
2. **Fill-in for combining like terms:**
- For \(y\): \(-14\)
- For the last term: \(-1\)

Thus:
-6x/7 - 14/28 y --> -6x/7 - 1/2 y