Which expressions are equivalent to
\[5(-2k-3)+2k\] ?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
\[(-5\cdot3)-8k\]
A
\[(-5\cdot3)-8k\]
(Choice B)
\[-15\]
B
\[-15\]
(Choice C) None of the above
C
None of the above
To simplify the expression, we distribute the 5 to the terms inside the parentheses:
\[5(-2k-3) + 2k = -10k - 15 + 2k.\]
Now, we combine like terms:
\[-10k - 15 + 2k = -8k - 15.\]
Thus, the expression is equivalent to $ \boxed{(-5\cdot3)-8k} $.
To simplify the expression \(5(-2k-3)+2k\), we can start by distributing the 5 to the terms inside the parentheses:
\[5 \cdot (-2k) + 5 \cdot (-3) + 2k\]
This gives us:
\[-10k - 15 + 2k\]
Next, we can combine like terms by adding the coefficients of k:
\[-10k + 2k - 15\]
This simplifies to:
\[-8k - 15\]
Therefore, the expression \(5(-2k-3)+2k\) is equivalent to \(-8k - 15\).
So the correct answer is:
(Choice A) \(-5 \cdot 3 - 8k\)
A \(-5 \cdot 3 - 8k\)
To solve this problem, we need to simplify the given expression:
\[5(-2k-3) + 2k\]
Distribute the 5 to every term inside the parentheses:
\[(-10k - 15) + 2k\]
Combine like terms by adding the coefficients of the k terms:
\[-10k + 2k - 15\]
Combine like terms:
\[-8k - 15\]
Now, let's compare this simplified expression to the choices given:
(Choice A): \[(-5 \cdot 3) - 8k\]
This simplifies to \[-15 - 8k\]
(Choice B): \[-15\]
(Choice C): None of the above
Comparing the simplified expression \[-8k - 15\] to the given choices, we can see that:
- Choice A, \[-15 - 8k\], is equivalent to the simplified expression.
- Choice B, \[-15\], is also equivalent to the simplified expression.
Therefore, the expressions that are equivalent to \[5(-2k-3) + 2k\] are:
\[(-5 \cdot 3) - 8k\] (Choice A) and \[-15\] (Choice B).