Question
\( 36 x+54 \) Complete the statements. \( 9(4 x+6) \square \) equivalent to \( 36 x+54 \). \( 4(9 x+11) \square \) equivalent to \( 36 x+54 \). \( 18(2 x+3) \)
Ask by Pope Lynch. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 9(4x + 6) = 36x + 54 \)
\( 4(9x + 11) \neq 36x + 54 \)
\( 18(2x + 3) = 36x + 54 \)
Solution
To determine the equivalence of the expressions, we will simplify each expression step by step.
1. **For the first expression**: \( 9(4x + 6) \)
- Distribute \( 9 \) to both terms inside the parentheses:
\[
9(4x) + 9(6) = 36x + 54
\]
- Therefore, \( 9(4x + 6) \) is equivalent to \( 36x + 54 \).
2. **For the second expression**: \( 4(9x + 11) \)
- Distribute \( 4 \) to both terms inside the parentheses:
\[
4(9x) + 4(11) = 36x + 44
\]
- Therefore, \( 4(9x + 11) \) is **not** equivalent to \( 36x + 54 \).
3. **For the third expression**: \( 18(2x + 3) \)
- Distribute \( 18 \) to both terms inside the parentheses:
\[
18(2x) + 18(3) = 36x + 54
\]
- Therefore, \( 18(2x + 3) \) is equivalent to \( 36x + 54 \).
### Summary of Equivalences:
- \( 9(4x + 6) \) is equivalent to \( 36x + 54 \).
- \( 4(9x + 11) \) is **not** equivalent to \( 36x + 54 \).
- \( 18(2x + 3) \) is equivalent to \( 36x + 54 \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To complete the statements, we can factor the expression \( 36x + 54 \) in different ways. For the first statement, we see that \( 9(4x + 6) \) is equivalent to \( 36x + 54 \) when you expand it: \( 9 \cdot 4x + 9 \cdot 6 = 36x + 54 \), so the first box is \( = \). In the second statement, \( 4(9x + 11) \) is not equivalent to \( 36x + 54 \) because if you expand \( 4(9x + 11) \), you get \( 36x + 44 \), not \( 36x + 54 \). Thus, the second box is \( \neq \). Finally, for \( 18(2x + 3) \), when expanded, you will also find that it equals \( 36x + 54 \) as \( 18 \cdot 2x + 18 \cdot 3 = 36x + 54 \), confirming that it is equivalent.
