Question

Which of the following is an example of an equation with no solution

3x + 4 = 4x + 3

3x + = 3x + 4

3x + 4 = 3x + 3

4x + 3 = 3x + 3

Answer 1

[AI-generated answer — Bot GPT 3.5]

The equation "3x + 4 = 4x + 3" is an example of an equation with no solution.

Answer 2

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

An example of an equation with no solution is when the equation leads to a contradiction. Let's analyze each given equation to determine which one has no solution:

1) 3x + 4 = 4x + 3:
To solve this equation, we can subtract 3x from both sides to eliminate the x terms:
3x + 4 - 3x = 4x + 3 - 3x
4 = x + 3
Next, subtract 3 from both sides to isolate the variable:
4 - 3 = x + 3 - 3
1 = x
Therefore, this equation has a solution of x = 1.

2) 3x + = 3x + 4:
This equation seems to be incomplete or missing a term. Without a complete equation, we cannot determine a solution or conclude that it has no solution.

3) 3x + 4 = 3x + 3:
We can simplify this equation by subtracting 3x from both sides:
3x + 4 - 3x = 3x + 3 - 3x
4 = 3
There is a contradiction here since 4 does not equal 3. Hence, this equation has no solution.

4) 4x + 3 = 3x + 3:
By subtracting 3x from both sides, we can simplify the equation:
4x + 3 - 3x = 3x + 3 - 3x
x + 3 = 3
Next, subtract 3 from both sides to isolate the variable:
x + 3 - 3 = 3 - 3
x = 0
Therefore, this equation has a solution of x = 0.

From the given options, the equation that has no solution is: 3x + 4 = 3x + 3.

Answer 3

[AI-generated answer — Explain Bot]

To determine which equation has no solution, we need to check which equation leads to an inconsistency or contradiction. In other words, we need to find the equation where the variable (x) cancels out on both sides, leaving a false statement.

Let's check each equation one by one:

1) 3x + 4 = 4x + 3
To solve this equation, let's move all the variables to one side and constants to the other side.
3x - 4x = 3 - 4
Simplifying further,
-x = -1
Now, we multiply both sides by -1 to isolate the variable.
x = 1
In this case, we found a solution, so this equation does have a solution.

2) 3x + = 3x + 4
There seems to be a typing mistake in this equation as there is a missing term on the left-hand side. Without a complete equation, we cannot determine if it has a solution or not.

3) 3x + 4 = 3x + 3
Let's solve this equation in a similar manner as the first equation.
3x - 3x = 3 - 4
Simplifying further,
0 = -1
This is a false statement since zero cannot equal -1. Therefore, this equation has no solution.

4) 4x + 3 = 3x + 3
To solve this equation, we follow the same steps as before.
4x - 3x = 3 - 3
Simplifying further,
x = 0
In this case, we found a solution, so this equation does have a solution.

So, out of the given options, the equation with no solution is 3x + 4 = 3x + 3.