What value of b would make the expressions (16k+14)−(13k−2)−(8k+4) and bk+8 equivalent?
To make the expressions \((16k+14) - (13k-2) - (8k+4)\) and \(bk+8\) equivalent, we need to set them equal to each other and solve for \(b\).
So we have:
\((16k+14) - (13k-2) - (8k+4) = bk+8\)
Expanding the expressions in parentheses, we get:
\(16k + 14 - 13k + 2 - 8k - 4 = bk + 8\)
Combining like terms, we simplify:
\(-5k + 12 = bk + 8\)
Next, we can isolate \(bk\) by moving the constant terms to the other side of the equation:
\(bk = -5k + 12 - 8\)
\(bk = -5k + 4\)
Finally, we can solve for \(b\) by dividing both sides of the equation by \(k\):
\(b = \frac{-5k + 4}{k}\)
Thus, the value of \(b\) that would make the expressions \((16k+14) - (13k-2) - (8k+4)\) and \(bk+8\) equivalent is \(\frac{-5k + 4}{k}\).