Question
8k+38=−3(−6−4k)
infinite solutions or none
infinite solutions or none
Answers
GPT 3.5
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.
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.