Question

Determine the missing values that would make this equation have infinite amount of solutions. Both answers will be integers. (6 points) 2(5x+6)+2=-6x+_x+_

Answer 1

[AI-generated answer — Bot GPT 3.5]

To have an infinite amount of solutions, the missing values must make the equation true regardless of the value of x.

Starting with the equation:
2(5x+6)+2=-6x+_x+_

Distributing the 2 on the left side:
10x + 12 + 2 = -6x + _x + _

Simplifying the equation:
10x + 14 = -6x + _x + _

Combining like terms:
16x + 14 = _x + _

To have an infinite amount of solutions, the coefficients of x on both sides must be equal. Therefore, we can set 16x = _x.

Solving for x:
16x = _x
16 = _

So, the missing values are 16 and 16.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To have an infinite number of solutions, the equation must be true for any value of x. In other words, we need the equation to simplify to something like 0 = 0.

Let's simplify the given equation step-by-step:

2(5x + 6) + 2 = -6x + _x + _

First, distribute the 2 to the terms inside the parentheses:

10x + 12 + 2 = -6x + _x + _

Combine like terms:

10x + 14 = -6x + _x + _

Next, let's gather like terms on one side of the equation. To do that, let's add 6x to both sides:

10x + 6x + 14 = -6x + 6x + _x + _

Combine like terms:

16x + 14 = 7x + _

To eliminate the variables on the right side of the equation, we need to subtract 7x from both sides:

16x + 14 - 7x = 7x + _x - 7x

Combine like terms:

9x + 14 = _x

Now, in order for the equation to have an infinite number of solutions, the coefficient of x on one side should cancel out when compared to the coefficient of x on the other side. In this case, we have 9x on the left side and _x on the right side. For them to cancel out, the missing value should be -9, since -9x + 9x = 0.

Thus, the missing values that would make this equation have an infinite number of solutions are -9 and 0.

Answer 3

[AI-generated answer — Explain Bot]

To determine the missing values that would make the equation have an infinite number of solutions, we need to set up the equation and solve for the missing values.

Starting with the given equation:
2(5x+6) + 2 = -6x + _x + _

Let's begin by simplifying both sides of the equation:
10x + 12 + 2 = -6x + _x + _

Combining like terms:
10x + 14 = -6x + _x + _

Next, we'll rearrange the equation to isolate the variables on one side and the constants on the other side:
10x + 6x + _x = -14

Combine the x terms:
16x + _x = -14

To have an infinite number of solutions, the coefficients of x on both sides of the equation must be equal. In this case, 16 and _ must be equal. Therefore, filling in the missing values:
16x + 16x = -14

Combine the x terms:
32x = -14

Now, solve for x:
x = -14/32

Simplifying the fraction:
x = -7/16

Thus, the missing values that would make the equation have an infinite number of solutions are -14 and -7/16.