Question

Which expression is equivalent to 5 (a - 3b) - 4a + b?
A. -a - 2b
B. a - 14b
C. 9a - b
D. 9a - 9b

Answer 1

To simplify the expression \( 5(a - 3b) - 4a + b \), we start by distributing \( 5 \) in the term \( 5(a - 3b) \):

\[
5(a - 3b) = 5a - 15b
\]

Now, we can rewrite the entire expression:

\[
5(a - 3b) - 4a + b = (5a - 15b) - 4a + b
\]

Now, combine the like terms for \( a \):

\[
5a - 4a = 1a \quad \text{or simply} \quad a
\]

Next, combine the like terms for \( b \):

\[
-15b + b = -15b + 1b = -14b
\]

Putting it all together, we have:

\[
a - 14b
\]

Therefore, the expression \( 5(a - 3b) - 4a + b \) simplifies to \( a - 14b \).

The answer is \( \boxed{B} \).