Question

Complete the following stepped out solution to show that 3 + 7 (p - 11) is equivalent to 7 • p - 74. 3 + 7 (p - 11) 3 + 7 • p - 7 • blank apply the destructive property and multiply 3 + 7 • p - blank 7 • p + 3 - blank apply the commutative property of addition and subtract 7 • p - 74

Answer 1

Let's complete the stepped-out solution step by step to show that \(3 + 7 (p - 11)\) is equivalent to \(7 \cdot p - 74\).

1. **Start with the expression**:
\[
3 + 7 (p - 11)
\]

2. **Apply the distributive property to multiply** \(7\) by each term inside the parentheses**:
\[
3 + 7 \cdot p - 7 \cdot 11
\]
(Here, you would fill in the blank with \(11\)).

3. **Calculate \(7 \cdot 11\)**:
\[
3 + 7 \cdot p - 77
\]
(You fill the second blank with \(77\)).

4. **Now, combine the constant terms \(3\) and \(-77\)**:
\[
7 \cdot p + 3 - 77
\]
(Here, the third blank is filled with \(77\)).

5. **Combine the constants \(3 - 77\)**:
\[
7 \cdot p - 74
\]

Thus, the final result confirms our equivalence:
\[
3 + 7 (p - 11) = 7 \cdot p - 74
\]

To summarize:
- First blank: \(11\)
- Second blank: \(77\)
- Third blank: \(74\)

Therefore, the completed stepped-out solution is:

1. \(3 + 7(p - 11)\)
2. \(3 + 7 \cdot p - 7 \cdot 11\) (fill in \(11\))
3. \(3 + 7 \cdot p - 77\) (fill in \(77\))
4. \(7 \cdot p + 3 - 77\)
5. \(7 \cdot p - 74\)