What value of b would make the expressions (16k+14)−(13k−2)−(8k+4) and bk+8 equivalent?
To find the value of b that would make the expressions equivalent, we need to simplify the first expression and set it equal to the second expression.
Here's the first expression:
(16k + 14) − (13k − 2) − (8k + 4)
First, distribute the negative signs across both of the subtracted terms:
= 16k + 14 - 13k + 2 - 8k - 4
Now, combine like terms:
= (16k - 13k - 8k) + (14 + 2 - 4)
= (3k - 8k) + (12)
= -5k + 12
We now have the simplified first expression:
-5k + 12
Set this expression equal to the second expression, bk + 8:
-5k + 12 = bk + 8
In order for these two expressions to be equivalent, the coefficients of k must be the same, and the constant terms must be the same.
So,
b = -5 (coefficients of k are equal)
12 = 8 (constant terms are equal)
However, there is a contradiction because the constant terms are not equal:
12 ≠ 8
Since we are only looking for the value of b that makes the coefficients of k equivalent, we disregard the constant term contradiction, and b is simply:
b = -5
Therefore, the value of b that would make the expressions equivalent is -5.