Question

what value of b would make the expression?
(16k + 14) - (13k + 4) and bk + 8 equivalent?

Answer 1

To find the value of \( b \) that makes the expressions \( (16k + 14) - (13k + 4) \) and \( bk + 8 \) equivalent, we first simplify the left-hand expression:

\[
(16k + 14) - (13k + 4) = 16k + 14 - 13k - 4
\]

Now, combine like terms:

\[
= (16k - 13k) + (14 - 4) = 3k + 10
\]

So, the expression simplifies to:

\[
3k + 10
\]

Next, we want to set this equal to the right-hand expression, \( bk + 8 \):

\[
3k + 10 = bk + 8
\]

Now, we can equate the coefficients of \( k \) and the constant terms from both sides.

1. From the \( k \) terms:

\[
3 = b
\]

2. From the constant terms:

\[
10 = 8
\]

The second equation \( 10 = 8 \) is not valid; however, we need \( b \) to satisfy the first equation.

Thus, the value of \( b \) that makes the expressions equivalent is:

\[
\boxed{3}
\]