Question
Which expressions are equivalent to \( 5+(-3)(6 x-5) \) ? Choose all answers that apply: \[ \begin{array}{l}\text { A } 18 x-20 \\ \text { B None of the above }\end{array} \]
Ask by Herrera Franklin. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The correct answer is B: None of the above.
Solution
We want to simplify the expression:
5 + (–3)(6x – 5)
Step 1. Multiply (–3) by the terms inside (6x – 5):
5 – 18x + 15
Step 2. Combine like terms (the constants 5 and 15):
–18x + 20 or 20 – 18x
The answer we obtain, –18x + 20, is not the same as option A, 18x – 20. Since option B is "None of the above," the only correct answer is option B.
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Simplify this solution Beyond the Answer
To simplify \( 5+(-3)(6 x-5) \), we first distribute \(-3\) inside the parentheses: \[ 5 + (-3)(6x) + (-3)(-5) = 5 - 18x + 15 \] Now, combine like terms: \[ 5 + 15 - 18x = 20 - 18x \] So, the expression simplifies to \( 20 - 18x \). Now, we can check the options: A: \( 18x - 20 \) is not equivalent to \( 20 - 18x \). B: "None of the above" is correct because \( 20 - 18x \) is not listed. The answer is option **B**.
