What value of b would make the expressions (16k + 14) - (13k - 12) - (8k + 4) and bk + 8 equivalent?
To find the value of b that would make the expressions (16k + 14) - (13k - 12) - (8k + 4) and bk + 8 equivalent, we need to compare the given expressions and the expression bk + 8.
First, simplify the expression (16k + 14) - (13k - 12) - (8k + 4):
= 16k + 14 - 13k + 12 - 8k - 4
= 16k - 13k - 8k + 14 + 12 - 4
= (16 - 13 - 8)k + 14 + 12 - 4
= (-5k) + 22
Next, set this simplified expression equal to bk + 8:
(-5k) + 22 = bk + 8
To find the value of b, we need the coefficients of k on both sides of the equation to be equal.
Comparing the coefficients of k on both sides of the equation, we have:
-5 = b
Therefore, the value of b that would make the expressions (16k + 14) - (13k - 12) - (8k + 4) and bk + 8 equivalent is -5.