Fill in the blanks!

Question

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.