Question
26. Which too expressions are equivalent to \( 7 p+4 p+p+3 p \) ? A \( 7 p+4 p+3 p \) B \( 7 p+4 p+4 p \) C \( 11 p+3 p \) D \( 14 p \) E \( 15 p \quad 77+(q+?+3)=(+4+-3) p \)
Ask by Weaver Sullivan. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The equivalent expressions are B (\(7p + 4p + 4p\)) and E (\(15p\)).
Solution
To determine which expressions are equivalent to \( 7p + 4p + p + 3p \), let's simplify the original expression first:
\[
7p + 4p + p + 3p = (7 + 4 + 1 + 3)p = 15p
\]
Now, let's evaluate each of the provided options:
- **A. \( 7p + 4p + 3p \)**
\[
7p + 4p + 3p = (7 + 4 + 3)p = 14p \quad \text{(Not equivalent)}
\]
- **B. \( 7p + 4p + 4p \)**
\[
7p + 4p + 4p = (7 + 4 + 4)p = 15p \quad \text{(Equivalent)}
\]
- **C. \( 11p + 3p \)**
\[
11p + 3p = (11 + 3)p = 14p \quad \text{(Not equivalent)}
\]
- **D. \( 14p \)**
\[
14p \quad \text{(Not equivalent)}
\]
- **E. \( 15p \)**
\[
15p \quad \text{(Equivalent)}
\]
**Conclusion:**
The expressions **B** and **E** are equivalent to \( 7p + 4p + p + 3p \).
**Equivalent Expressions:**
- **B. \( 7p + 4p + 4p \)**
- **E. \( 15p \)**
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To simplify the expression \( 7 p + 4 p + p + 3 p \), we first combine like terms. Adding the coefficients together gives: \( 7 + 4 + 1 + 3 = 15 \). Thus, the expression simplifies to \( 15 p \). Now, let's analyze the options: A: \( 7 p + 4 p + 3 p = 14 p \) (not equivalent) B: \( 7 p + 4 p + 4 p = 15 p \) (equivalent) C: \( 11 p + 3 p = 14 p \) (not equivalent) D: \( 14 p \) (not equivalent) E: The expression \( 15 p \) is confirmed. So, the expressions that are equivalent to \( 7 p + 4 p + p + 3 p \) are options B \( 7 p + 4 p + 4 p \) and E which confirms \( 15 p \). Thus, the equivalent expressions are B and E.
