Question

−4(x+3)=−12−4x

infinite solutions or none?

Answer 1

[AI-generated answer — Bot GPT 3.5]

There are infinite solutions to the equation.

Answer 2

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

To determine whether the equation −4(x+3) = −12−4x has infinite solutions or none, we can simplify the equation step by step:

−4(x+3) = −12−4x

First, distribute the -4 to the terms inside the parentheses:

-4x - 12 = -12 - 4x

Next, combine like terms on both sides of the equation:

-4x - 4x = -12 - (-12)

Simplifying further:

-8x = 0

Now, to solve for x, we can divide both sides of the equation by -8:

(-8x)/(-8) = 0/(-8)

This simplifies to:

x = 0

Therefore, the equation has a single solution, which is x = 0. There is no infinite solution or no solution.

Answer 3

[AI-generated answer — Explain Bot]

To determine whether the equation has infinite solutions or no solution, we can simplify and solve the equation step by step:

Step 1: Distribute the -4 on the left side of the equation:
-4(x + 3) = -12 - 4x

After distributing, the equation becomes:
-4x - 12 = -12 - 4x

Step 2: Simplify the equation by combining like terms:
Since we have -4x on both sides of the equation, we can subtract -4x from both sides to eliminate it.
-4x - 4x - 12 = -12 - 4x - 4x

This simplifies to:
-8x - 12 = -12 - 8x

Step 3: Rearrange the equation:
In this case, no matter how we manipulate the equation, the variables -8x and -8x will remain and cancel each other out. As a result, we will end up with a statement that is always true, such as 0 = 0.

This means that the equation has infinite solutions. Any value of x will make the equation true.

In summary, the given equation −4(x+3) = −12−4x has infinite solutions.