Question

Which of the following equations has no solutions?(1 point) Responses 6x+4=6x+4 6 x plus 4 equals 6 x plus 4 −6x+4=6x+3 negative 6 x plus 4 equals 6 x plus 3 −6x+4=−6x+3 negative 6 x plus 4 equals negative 6 x plus 3 6x+3=−6x+3 6 x plus 3 equals negative 6 x plus 3

Answer 1

The equation that has no solutions is -6x+4 = -6x+3.

To understand why this equation has no solutions, let's analyze it step by step.

First, let's simplify both sides of the equation:

-6x + 4 = -6x + 3

Next, let's isolate the variable by subtracting -6x from both sides:

-6x + 6x + 4 = -6x + 6x + 3

This simplifies to:

4 = 3

Now, we can clearly see that the equation is not true. The left side of the equation is 4, while the right side is 3. Since these two values are not equal, there are no values of x that can satisfy this equation. Therefore, the equation has no solutions.

In summary, the equation -6x+4 = -6x+3 has no solutions because it leads to a contradiction where 4 is not equal to 3.

Answer 2

-6x + 4 = -6x + 3

Explanation:

Let's analyze each of the equations:

1. 6x + 4 = 6x + 4

This equation simplifies to 0 = 0. It's always true, so it has infinitely many solutions.

Every real number is a solution.

2. -6x + 4 = 6x + 3

By simplifying this equation, we can see that -6x = 6x - 1, which results in
`\sf x = -(1)/(12)`. This equation has one solution.

3. -6x + 4 = -6x + 3

By simplifying this equation, we get 4 = 3. This equation is inconsistent and has no solutions. It represents an impossible scenario.

4. 6x + 3 = -6x + 3

By simplifying this equation, we get 6x = -6x. This equation has only one solution, which is x = 0.

So, the equation with no solutions is -6x + 4 = -6x + 3.