Simplify to create an equivalent expression.
\[\qquad{8(10-6q)+3(-7q-2)}\]
Choose 1 answer:
Choose 1 answer:
(Choice A)
\[-69q+78\]
A
\[-69q+78\]
(Choice B)
\[-55q+74\]
B
\[-55q+74\]
(Choice C)
\[-69q+74\]
C
\[-69q+74\]
(Choice D)
\[69q+74\]
D
\[69q+74\]
To simplify the expression, we distribute the coefficients:
\begin{align*}
8(10-6q)+3(-7q-2) &= 80-48q-21q-6 \\
&= 74-69q.
\end{align*}The correct simplified expression is $\boxed{-69q + 74}$.
To simplify the expression, we need to distribute the numbers outside the parentheses to the numbers inside the parentheses and then combine like terms.
Step 1: Multiply 8 by each term inside the first set of parentheses:
\[8(10-6q) = 80 - 48q.\]
Step 2: Multiply 3 by each term inside the second set of parentheses:
\[3(-7q-2) = -21q - 6.\]
Now, we have:
\[80 - 48q + (-21q) - 6.\]
Step 3: Combine like terms by adding or subtracting coefficients of the same variable:
\[-48q - 21q = -69q.\]
\[80 - 6 = 74.\]
The simplified expression is \[-69q + 74.\]
Therefore, the correct answer is (Choice C) \[-69q + 74\].
To simplify the expression, we can distribute the numbers outside the parentheses to the terms inside.
Starting with the first term:
\[8(10-6q) = 80 - 48q\]
Next, simplify the second term:
\[3(-7q-2) = -21q - 6\]
Combining both terms, we have:
\[80 - 48q + (-21q) - 6 = 80 - 48q - 21q - 6\]
Combining like terms, we get:
\[80 - 48q - 21q - 6 = 74 - 69q\]
Therefore, the simplified expression is \[-69q + 74\].
So the correct answer is choice C, \[-69q + 74\].