Which of the following is an example of an equation with no solution
3x+4=3x+4
3x+4=4x+3
4x+3=3x+3
3x+4=3x+3
An example of an equation with no solution is: 4x+3=3x+3.
The equation that has no solution is:
3x + 4 = 3x + 3
To determine if an equation has no solution, we need to check if the equation is contradictory. This means that the equation represents an impossible situation where the two sides of the equation will never be equal, regardless of the value we assign to the variable.
Let's evaluate each option one by one:
1. 3x + 4 = 3x + 4
This equation is an identity since both sides are equal, regardless of the value of x. Therefore, it has infinite solutions, not no solution.
2. 3x + 4 = 4x + 3
To determine if this equation has a solution, we can start by simplifying both sides by combining like terms:
3x + 4 - 3x = 4x + 3 - 3x
4 = x + 3
In this case, we can subtract 3 from both sides to isolate the x-variable:
4 - 3 = x + 3 - 3
1 = x
Therefore, this equation has a solution, x = 1.
3. 4x + 3 = 3x + 3
Like before, we can simplify the equation:
4x + 3 - 3x = 3x + 3 - 3x
x + 3 = 3
Subtracting 3 from both sides gives us:
x + 3 - 3 = 3 - 3
x = 0
Therefore, this equation has a solution, x = 0.
4. 3x + 4 = 3x + 3
Similar to the previous steps, we simplify the equation:
3x + 4 - 3x = 3x + 3 - 3x
4 = 3
However, 4 is not equal to 3. This contradiction indicates that there is no solution for this equation.
Thus, the equation 3x + 4 = 3x + 3 is an example of an equation with no solution.