Question

Fill in the blanks!

Subtract 3/7y - x/4 + 10 from 13/4 x - y/7 - 23.

(13/4 x -y/7 - 23) - (3/7 y - x/4 + 10)
13/4 x - y/7 - 23 - 3/7 y + x/4 - 10

x-terms
13/4 x + x/_
x (13/4 + 1/4)
x (14/4)
_/2x

y-terms
-y/7-3/7y
+y(-1/7-3/7)
+y(-4/_)
-4/7y

constants
-23 - _
-_
-33
-33

The expression 7/2x - 4/7 y - 33 represents the difference.

Answer 1

Let's fill in the blanks step by step, starting with the expression:

\[
(13/4 x - y/7 - 23) - (3/7 y - x/4 + 10)
\]

1. Distributing the negative sign:
\[
13/4 x - y/7 - 23 - 3/7 y + x/4 - 10
\]

2. Combine like terms for the \(x\)-terms:
- We have \(13/4 x + x/4\).
- To add these, we need a common denominator. The common denominator of 4 is 4:
\[
13/4 x + 1/4 x = (13/4 + 1/4)x = (14/4)x = \frac{7}{2}x
\]

So, for the \(x\)-terms:
\[
13/4 x + x/4 = \frac{7}{2}x
\]

3. Combine the \(y\)-terms:
- We have \(-y/7 - 3/7 y\).
- Combining these gives:
\[
-y/7 - 3/7 y = -1/7 y - 3/7 y = -\frac{4}{7}y
\]

So, for the \(y\)-terms:
\[
-y/7 - 3/7 y = -\frac{4}{7} y
\]

4. Combine the constants:
- We have \(-23 - 10\).
- This gives:
\[
-23 - 10 = -33
\]

So, for the constants:
\[
-23 - 10 = -33
\]

Putting it all together, we have:

\[
\frac{7}{2} x - \frac{4}{7} y - 33
\]

Thus, filling in the blanks, the final expression is:

The expression \( \frac{7}{2}x - \frac{4}{7}y - 33 \) represents the difference.