Question
How many solutions does this equation have? 8+3(x-6)=-2x3x-4
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Answers
Answered by
GPT 3.5
First, simplify the left side of the equation:
8 + 3(x-6) = -2x3x - 4
8 + 3x - 18 = -6x - 4
3x - 10 = -6x - 4
Next, combine like terms:
3x + 6x = 10 - 4
9x = 6
x = 6/9
x = 2/3
Therefore, the equation has one solution, x = 2/3.
8 + 3(x-6) = -2x3x - 4
8 + 3x - 18 = -6x - 4
3x - 10 = -6x - 4
Next, combine like terms:
3x + 6x = 10 - 4
9x = 6
x = 6/9
x = 2/3
Therefore, the equation has one solution, x = 2/3.
Answer
answer is no solutions
Answered by
GPT 3.5
Apologies for the error in my previous response. Let's re-evaluate the equation to determine the correct number of solutions.
Given equation: 8 + 3(x-6) = -2x(3x-4)
Expanding both sides:
8 + 3x - 18 = -6x^2 + 8x
-10 + 3x = -6x^2 + 8x
Rearranging terms:
6x^2 - 5x - 10 = 0
This is a quadratic equation in the form of ax^2 + bx + c = 0. To determine the number of solutions, we can use the discriminant:
Δ = b^2 - 4ac
Δ = (-5)^2 - 4(6)(-10)
Δ = 25 + 240
Δ = 265
Since the discriminant Δ is positive (265 > 0), the equation has two distinct real solutions. Therefore, the correct statement is that the equation has two solutions.
Given equation: 8 + 3(x-6) = -2x(3x-4)
Expanding both sides:
8 + 3x - 18 = -6x^2 + 8x
-10 + 3x = -6x^2 + 8x
Rearranging terms:
6x^2 - 5x - 10 = 0
This is a quadratic equation in the form of ax^2 + bx + c = 0. To determine the number of solutions, we can use the discriminant:
Δ = b^2 - 4ac
Δ = (-5)^2 - 4(6)(-10)
Δ = 25 + 240
Δ = 265
Since the discriminant Δ is positive (265 > 0), the equation has two distinct real solutions. Therefore, the correct statement is that the equation has two solutions.