Question

8k+38=−3(−6−4k)
infinite solutions or none

Answer 1

To determine if the equation has infinite solutions or none, we need to solve it and see how many solutions we obtain.

Let's simplify the equation step by step:

8k + 38 = -3(-6 - 4k)

Distribute -3 across the terms in the parentheses:

8k + 38 = 18 + 12k

Combine like terms:

8k - 12k = 18 - 38

-4k = -20

To solve for k, we need to divide both sides of the equation by -4:

k = (-20) / (-4)

k = 5

By substituting k = 5 back into the original equation, we can verify if it holds true:

8(5) + 38 = -3(-6 - 4(5))
40 + 38 = -3(-6 - 20)
78 = -3(-26)
78 = 78

Since the equation holds true for k = 5, we can conclude that the original equation has one solution, which is k = 5.