Question

Fill in the blanks!

Add the expressions 3/7y - x/4 + 10 amd 13x/4 - y/7 - 23.
3/7 y - x/4 + 10 + 13x/4 - y/7 - 23

y-terms
3/7 y - y/_
y (3/7 -1/7)
2/7 _

x-terms
-x/4 + 13x/4
x(-1/4+_/4)
+3x

Constants
+_-23
-13
-13

The answer is 2/7y+3x-13.

Answer 1

Let's fill in the blanks step by step for the given problem.

1. **y-terms**:
\[
3/7y - y/7
\]
To combine these terms:
\[
3/7y - y/7 = y(3/7 - 1/7)
\]
Here, \(1/7\) comes from \(-y/7\).
So:
\[
3/7 - 1/7 = 2/7
\]
Thus, you have:
\[
2/7y
\]

2. **x-terms**:
\[
-x/4 + 13x/4
\]
To combine these terms:
\[
x(-1/4 + 13/4) = x(12/4) = 3x
\]

3. **Constants**:
\[
10 - 23
\]
This simplifies to:
\[
10 - 23 = -13
\]

Now, putting everything together, the combined expression from the three parts is:

\[
\frac{2}{7}y + 3x - 13
\]

So the completed version is:

- y-terms: \( - y/7 \) and \( 2/7 \)
- x-terms: \( 13/4 \)
- Constants: \( 10 \)

The final answer to the addition of the expressions is:

\[
\frac{2}{7}y + 3x - 13
\]