Question

Complete the following stepped-out solution to show that 3+7(p -11) is equivalent to 7*p-74.
3+*p-7* Apply the Distributive Property and multiply
3+7*p-
7*p+3- Apply the Commutative Property of Addition and subtract

Answer 1

Let's start with the expression \( 3 + 7(p - 11) \) and simplify it step by step to show that it is equivalent to \( 7p - 74 \).

1. **Apply the Distributive Property:**
Distribute \( 7 \) to both terms in the parentheses:
\[
3 + 7(p - 11) = 3 + 7p - 7 \cdot 11
\]
\[
= 3 + 7p - 77
\]

2. **Combine like terms:**
Combine \( 3 \) and \( -77 \):
\[
3 - 77 + 7p = -74 + 7p
\]

3. **Rearrange the expression:**
Using the Commutative Property of Addition, we can write:
\[
7p - 74
\]

Thus, the complete expression \( 3 + 7(p - 11) \) simplifies to \( 7p - 74 \). This shows that they are equivalent.

In mathematical form, you have:
\[
3 + 7(p - 11) = 7p - 74
\]