Simplify to create an equivalent expression.
\[\qquad{2(-14+r)-(-3r-5)}\]
Choose 1 answer:
Choose 1 answer:
(Choice A)
\[5r-23\]
A
\[5r-23\]
(Choice B)
\[5r-33\]
B
\[5r-33\]
(Choice C)
\[-5r-23\]
C
\[-5r-23\]
(Choice D)
\[5r+23\]
D
\[5r+23\]
We distribute the 2 and the negative sign in front of the second set of parentheses to get $-28+2r-(-3r-5)$. We simplify the expression inside the parentheses by distributing the negative sign to get $-28+2r+3r+5$. Finally, we combine like terms to get $5r-23$. Thus, the simplified expression is $\boxed{5r-23}$.
To simplify the expression, we can start by applying the distributive property to the terms inside the parentheses. We have:
\[2(-14 + r) - (-3r - 5)\]
Simplifying inside the first set of parentheses, we have:
\[2(-14 + r) = 2(-14) + 2(r) = -28 + 2r\]
Next, we need to distribute the negative sign in front of the second set of parentheses:
\[-(-3r - 5) = -1*(-3r) - 1*(-5) = 3r + 5\]
Now we can combine the terms obtained above:
\[-28 + 2r - (3r + 5)\]
To simplify further, we can group the terms involving 'r' together:
\[2r - 3r - 28 - 5\]
Combining like terms, we get:
\[-r - 33\]
Therefore, the equivalent expression is \(-r - 33\), which matches with choice B. So the correct answer is \(\boxed{B: 5r-33}\).
To simplify the expression \[2(-14+r)-(-3r-5)\], we need to first distribute the 2 and distribute the negative sign inside the second set of parentheses. This gives us:
\[2 \cdot -14 + 2 \cdot r - (-3 \cdot r) - (-5)\]
Next, we simplify the expression:
\[-28 + 2r + 3r + 5\]
Combining like terms:
\[5r - 23\]
So, the simplified expression is \[5r-23\].
Therefore, the answer is (Choice A): \[5r-23\].